Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
708 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 243 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. #21446376 | C2 | semidirect |
| 4. #21445677 | C2 | semidirect |
| 6. #21445568 | C2 | semidirect |
| 7. C42×C8×C61 | C2 | semidirect |
| 108. C42×C8 | D61 | semidirect |
| 128. C61 | #21432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448316 | 2 |
| #21446425 | 2 |
| #21446376 | 2 |
| #21445677 | 2 |
| #21445586 | 2 |
| #21445568 | 2 |
| C42×C8×C61 | 2 |
| #21432 | 61 |