Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
394 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 120 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. C2×#16840651 | C2 | semidirect |
| 2. #21461366 | C2 | semidirect |
| 3. #21460779 | C2 | semidirect |
| 4. #21460777 | C2 | semidirect |
| 52. #135×C61 | C8 | semidirect |
| 170. C61 | #11597 | semidirect |
| 173. #135 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840651 | 2 |
| #21461366 | 2 |
| #21460779 | 2 |
| #21460777 | 2 |
| #135×Dic61 | 2 |
| #11597 | 61 |