Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
522 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 5. #16840628 | C4 | semidirect |
| 20. C2×C4×Dic61 | C8 | semidirect |
| 30. C2×C42×C61 | C8 | semidirect |
| 156. C61 | #7017 | semidirect |
| 174. C2×C42 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461709 | 2 |
| C4×#14519684 | 2 |
| #7017 | 61 |