Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
482 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 3. #21461370 | C2 | semidirect |
| 4. #21460652 | C2 | semidirect |
| 44. #100×C61 | C8 | semidirect |
| 68. M16×C61 | C2×C8 | semidirect |
| 149. C61 | #8835 | semidirect |
| 167. #100 | #92420 | semidirect |
| 191. M16 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462666 | 2 |
| #21461940 | 2 |
| #21461370 | 2 |
| #21460652 | 2 |
| #100×Dic61 | 2 |
| #8835 | 61 |