Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
436 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 436 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. #21461275 | C2 | semidirect |
| 3. #21461274 | C2 | semidirect |
| 4. #21461140 | C2 | semidirect |
| 5. #21461139 | C2 | semidirect |
| 6. #21461029 | C2 | semidirect |
| 214. C61 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519848 | 2 |
| #21461275 | 2 |
| #21461274 | 2 |
| #21461140 | 2 |
| #21461139 | 2 |
| #21461029 | 2 |
| #21456397 | 2 |
| #9726 | 61 |