Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 112 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. #21461368 | C2 | semidirect |
| 2. #21461123 | C2 | semidirect |
| 4. #21461063 | C2 | semidirect |
| 6. #21461022 | C2 | semidirect |
| 48. C2×#11758200 | C8 | semidirect |
| 227. C61 | #9667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461368 | 2 |
| #21461123 | 2 |
| #21461118 | 2 |
| #21461063 | 2 |
| #21461059 | 2 |
| #21461022 | 2 |
| C2×#16839853 | 2 |
| #9667 | 61 |