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. #16840784 | C4 | semidirect |
| 8. #16840766 | C4 | semidirect |
| 20. C4⋊#92420 | C2×C4 | semidirect |
| 69. C42×C61 | M16 | semidirect |
| 78. C4×Dic61 | M16 | semidirect |
| 150. C61 | #7867 | semidirect |
| 211. C42 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462496 | 2 |
| #21460647 | 2 |
| C43×D61 | 2 |
| #7867 | 61 |