Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
696 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 274 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. #21461916 | C2 | semidirect |
| 3. #21461872 | C2 | semidirect |
| 5. #21461751 | C2 | semidirect |
| 6. #21461746 | C2 | semidirect |
| 45. #126×C61 | C8 | semidirect |
| 66. C4⋊C4×C61 | C2×C8 | semidirect |
| 68. C42×C61 | C2×C8 | semidirect |
| 143. C61 | #23375 | semidirect |
| 150. #126 | #92420 | semidirect |
| 186. C4⋊C4 | C2×#92420 | semidirect |
| 194. C42 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461916 | 2 |
| #21461888 | 2 |
| #21461872 | 2 |
| #21461762 | 2 |
| #21461751 | 2 |
| #21461746 | 2 |
| #126×Dic61 | 2 |
| #23375 | 61 |