Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
668 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 147 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×#16840204 | C2 | semidirect |
| 2. #21457561 | C2 | semidirect |
| 3. #21448080 | C2 | semidirect |
| 4. #21447933 | C2 | semidirect |
| 5. #21447881 | C2 | semidirect |
| 6. #21447754 | C2 | semidirect |
| 7. #21447745 | C2 | semidirect |
| 8. #21447652 | C2 | semidirect |
| 9. C4×Q32×C61 | C2 | semidirect |
| 69. Q32×C61 | D4 | semidirect |
| 167. C4×Q32 | D61 | semidirect |
| 200. C61 | #33843 | semidirect |
| 225. Q32 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840204 | 2 |
| #21457561 | 2 |
| #21448080 | 2 |
| #21447933 | 2 |
| #21447881 | 2 |
| #21447754 | 2 |
| #21447745 | 2 |
| #21447652 | 2 |
| C4×Q32×C61 | 2 |
| #33843 | 61 |