Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
650 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21426457 | C2 | semidirect |
| 2. #21425016 | C2 | semidirect |
| 3. #21422604 | C2 | semidirect |
| 4. #21422539 | C2 | semidirect |
| 5. #21421988 | C2 | semidirect |
| 6. #21421953 | C2 | semidirect |
| 24. C59×#476 | C4 | semidirect |
| 25. C59×#459 | C4 | semidirect |
| 52. C4⋊Q8×C59 | C2×C4 | semidirect |
| 53. #127×C59 | C2×C4 | semidirect |
| 67. C4⋊C8×C59 | C2×C4 | semidirect |
| 135. D4×C59 | #104 | semidirect |
| 208. #476 | Dic59 | semidirect |
| 209. #459 | Dic59 | semidirect |
| 225. C59 | #9325 | semidirect |
| 232. C4⋊Q8 | C2×Dic59 | semidirect |
| 233. #127 | C2×Dic59 | semidirect |
| 254. C4⋊C8 | C2×Dic59 | semidirect |
| 332. D4 | #14273654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426457 | 2 |
| #21425016 | 2 |
| #21422604 | 2 |
| #21422539 | 2 |
| #21421988 | 2 |
| #21421953 | 2 |
| C59×#3109 | 2 |
| #9325 | 59 |