Number of Distinct Homomorphic Images in Coset Diagrams

<div>Homomorphic images <span class="nowrap"><svg height="17.6501pt" id="M530" style="vertical-align:-6.058701pt" version="1.1" viewbox="-0.0498162 -11.5914 19.3723 17.6501" width="19.3723pt" 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="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,-0.0091,9.841,3.784)"><path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 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="M454 384C454 521 378 635 249 635C118 635 40 519 40 420C40 313 115 234 225 234C242 234 261 238 285 250L353 286C319 140 205 45 61 23L68 -15C91 -15 156 -5 210 15C349 68 454 196 454 384ZM359 390C359 372 358 347 355 326C332 310 300 298 265 298C183 298 129 369 129 454C129 513 159 594 234 594C331 594 359 479 359 390Z"></path></g></svg>.</span></div>

Journal of Mathematics

Number of Distinct Homomorphic Images in Coset Diagrams

Figure 19