Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
564 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21433007 | C2 | semidirect |
| 2. #21426308 | C2 | semidirect |
| 3. #21426264 | C2 | semidirect |
| 4. #21426169 | C2 | semidirect |
| 5. #21426041 | C2 | semidirect |
| 6. #21425992 | C2 | semidirect |
| 7. #21425908 | C2 | semidirect |
| 8. C59×#3184 | C2 | semidirect |
| 18. #16837224 | C22 | semidirect |
| 19. #16837223 | C22 | semidirect |
| 20. #16837215 | C22 | semidirect |
| 23. #16837180 | C22 | semidirect |
| 25. C59×#498 | C22 | semidirect |
| 26. C59×#493 | C22 | semidirect |
| 31. C59×#442 | C22 | semidirect |
| 107. Dic236 | #41 | semidirect |
| 109. D472 | #41 | semidirect |
| 165. #3184 | D59 | semidirect |
| 182. #498 | C2×D59 | semidirect |
| 183. #493 | C2×D59 | semidirect |
| 192. #442 | C2×D59 | semidirect |
| 202. C59 | #33688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21433007 | 2 |
| #21426308 | 2 |
| #21426264 | 2 |
| #21426169 | 2 |
| #21426041 | 2 |
| #21425992 | 2 |
| #21425908 | 2 |
| C59×#3184 | 2 |
| #33688 | 59 |