Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16837842 | C2 | semidirect |
| 2. C22×#14273672 | C2 | semidirect |
| 4. #21432963 | C2 | semidirect |
| 5. #21426161 | C2 | semidirect |
| 6. #21426135 | C2 | semidirect |
| 7. #21425854 | C2 | semidirect |
| 8. #21425811 | C2 | semidirect |
| 9. C59×#2138 | C2 | semidirect |
| 16. C2×#14273673 | C22 | semidirect |
| 19. C2×#14273671 | C22 | semidirect |
| 25. #16837496 | C22 | semidirect |
| 28. Dic59⋊C16 | C22 | semidirect |
| 33. C59×#358 | C22 | semidirect |
| 34. C59×#357 | C22 | semidirect |
| 40. C2×Dic236 | D4 | semidirect |
| 180. #2138 | D59 | semidirect |
| 208. #358 | C2×D59 | semidirect |
| 210. #357 | C2×D59 | semidirect |
| 211. C59 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837842 | 2 |
| C22×#14273672 | 2 |
| #21434583 | 2 |
| #21432963 | 2 |
| #21426161 | 2 |
| #21426135 | 2 |
| #21425854 | 2 |
| #21425811 | 2 |
| C59×#2138 | 2 |
| #33587 | 59 |