Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
328 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 328 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. C2×#16840684 | C2 | semidirect |
| 4. C2×#16840654 | C2 | semidirect |
| 5. #21460864 | C2 | semidirect |
| 6. #21460860 | C2 | semidirect |
| 172. C61 | #13128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840684 | 2 |
| C2×#16840659 | 2 |
| C2×#16840654 | 2 |
| #21460864 | 2 |
| #21460860 | 2 |
| #21445601 | 2 |
| #13128 | 61 |