Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
922 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 2. #21460647 | C2 | semidirect |
| 4. #16840783 | C4 | semidirect |
| 8. #16840765 | C4 | semidirect |
| 20. C4⋊#92420 | C2×C4 | semidirect |
| 69. C42×C61 | M16 | semidirect |
| 81. C4×Dic61 | M16 | semidirect |
| 157. C61 | #7867 | semidirect |
| 224. C42 | #11758217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462495 | 2 |
| #21460647 | 2 |
| C2×C42×Dic61 | 2 |
| #7867 | 61 |