Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
712 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 323 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 |
|---|---|---|
| 2. #21422400 | C2 | semidirect |
| 3. #21422398 | C2 | semidirect |
| 4. #21422397 | C2 | semidirect |
| 5. #21422396 | C2 | semidirect |
| 6. #21422395 | C2 | semidirect |
| 7. C59×#1454 | C2 | semidirect |
| 18. #16837124 | C22 | semidirect |
| 19. #16837124 | C22 | semidirect |
| 20. #16837123 | C22 | semidirect |
| 21. C8×C59⋊C8 | C22 | semidirect |
| 23. C59×#322 | C22 | semidirect |
| 24. C82×C59 | C22 | semidirect |
| 101. #1454 | D59 | semidirect |
| 120. #322 | C2×D59 | semidirect |
| 122. C82 | C2×D59 | semidirect |
| 123. C59 | #17339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432724 | 2 |
| #21422400 | 2 |
| #21422398 | 2 |
| #21422397 | 2 |
| #21422396 | 2 |
| #21422395 | 2 |
| C59×#1454 | 2 |
| #17339 | 59 |