Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
498 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21432948 | C2 | semidirect |
| 2. #21425832 | C2 | semidirect |
| 3. #21425812 | C2 | semidirect |
| 4. #21424995 | C2 | semidirect |
| 5. #21422198 | C2 | semidirect |
| 6. #21422181 | C2 | semidirect |
| 24. C2×SD32×C59 | C4 | semidirect |
| 25. C2×D16×C59 | C4 | semidirect |
| 52. C2×Q16×C59 | C2×C4 | semidirect |
| 58. C2×D8×C59 | C2×C4 | semidirect |
| 66. C2×C16×C59 | C2×C4 | semidirect |
| 186. C2×SD32 | Dic59 | semidirect |
| 187. C2×D16 | Dic59 | semidirect |
| 200. C59 | #13033 | semidirect |
| 207. C2×Q16 | C2×Dic59 | semidirect |
| 213. C2×D8 | C2×Dic59 | semidirect |
| 231. C2×C16 | C2×Dic59 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432948 | 2 |
| #21425832 | 2 |
| #21425812 | 2 |
| #21424995 | 2 |
| #21422198 | 2 |
| #21422181 | 2 |
| C2×C59×#509 | 2 |
| #13033 | 59 |