Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21447869 | C2 | semidirect |
| 4. #21443889 | C2 | semidirect |
| 5. #21443867 | C2 | semidirect |
| 7. C8×Q16×C61 | C2 | semidirect |
| 112. C8×Q16 | D61 | semidirect |
| 135. C61 | #12429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447869 | 2 |
| #21447859 | 2 |
| #21445425 | 2 |
| #21443889 | 2 |
| #21443867 | 2 |
| #21443864 | 2 |
| C8×Q16×C61 | 2 |
| #12429 | 61 |