Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 84 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. C4×#14519848 | C2 | semidirect |
| 2. #21461277 | C2 | semidirect |
| 4. #21461143 | C2 | semidirect |
| 6. C8×#11758213 | C2 | semidirect |
| 206. C61 | #9723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519848 | 2 |
| #21461277 | 2 |
| #21461275 | 2 |
| #21461143 | 2 |
| #21461140 | 2 |
| C8×#11758213 | 2 |
| #21456381 | 2 |
| #9723 | 61 |