Number of Distinct Homomorphic Images in Coset Diagrams

<div>(a) Homomorphic images <span class="nowrap"><svg height="17.5849pt" id="M513" style="vertical-align:-5.9935pt" version="1.1" viewbox="-0.0498162 -11.5914 87.3405 17.5849" width="87.3405pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.841,-5.741)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.273,-5.741)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 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-3V55L134 254V256L512 456V514L75 281V230L512 -3Z"></path></g><g transform="matrix(.013,0,0,-0.013,52.477,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,62.435,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g><g transform="matrix(.013,0,0,-0.013,70.287,0)"><path d="M535 230V280H52V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,80.823,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z"></path></g></svg>.</span> (b) Homomorphic images <span class="nowrap"><svg height="17.5849pt" id="M514" style="vertical-align:-5.9935pt" version="1.1" viewbox="-0.0498162 -11.5914 87.3405 17.5849" width="87.3405pt" xmlns="http://www.w3.org/2000/svg" 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643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.08,5.885)"><path d="M449 167C449 258 386 306 319 343C359 372 385 398 393 407C411 429 423 458 423 487C423 569 352 635 256 635C143 635 72 555 72 471C72 401 112 353 177 316C145 294 106 265 92 252C72 231 47 202 47 157C47 50 134 -12 245 -12C334 -12 449 50 449 167ZM342 480C342 424 315 389 281 362C208 395 150 428 150 498C150 546 184 597 242 597C290 597 342 559 342 480ZM365 143C365 72 316 26 255 26C193 26 133 76 133 163C133 216 166 264 216 296C294 259 365 217 365 143Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.868,0)"><path d="M116 412C83 412 59 388 59 355C59 321 83 297 115 297S170 321 170 355C170 388 147 412 116 412ZM114 -12C147 -12 171 11 171 46C171 78 147 103 115 103C84 103 60 78 60 46C60 11 84 -12 114 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.464,0)"><path d="M238 681C243 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Journal of Mathematics

Number of Distinct Homomorphic Images in Coset Diagrams

Figure 18