Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
536 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 88 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×#14519865 | C2 | semidirect |
| 2. #21461274 | C2 | semidirect |
| 3. #21461165 | C2 | semidirect |
| 4. #21461157 | C2 | semidirect |
| 5. #21460705 | C2 | semidirect |
| 6. #21460650 | C2 | semidirect |
| 245. C61 | #9211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14519865 | 2 |
| #21461274 | 2 |
| #21461165 | 2 |
| #21461157 | 2 |
| #21460705 | 2 |
| #21460650 | 2 |
| #21455878 | 2 |
| #9211 | 61 |