Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 100 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. #21461366 | C2 | semidirect |
| 2. #21461120 | C2 | semidirect |
| 3. #21461118 | C2 | semidirect |
| 4. #21461060 | C2 | semidirect |
| 5. #21461059 | C2 | semidirect |
| 6. #21461032 | C2 | semidirect |
| 237. C61 | #9670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461366 | 2 |
| #21461120 | 2 |
| #21461118 | 2 |
| #21461060 | 2 |
| #21461059 | 2 |
| #21461032 | 2 |
| C2×#16839842 | 2 |
| #9670 | 61 |