Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21456347 | C2 | semidirect |
| 4. #21443926 | C2 | semidirect |
| 5. #21443921 | C2 | semidirect |
| 6. #21443906 | C2 | semidirect |
| 53. C2×Q16×C61 | Q8 | semidirect |
| 55. C2×D8×C61 | Q8 | semidirect |
| 181. C61 | #13374 | semidirect |
| 187. C2×Q16 | Dic122 | semidirect |
| 189. C2×D8 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456347 | 2 |
| #21447555 | 2 |
| #21446718 | 2 |
| #21443926 | 2 |
| #21443921 | 2 |
| #21443906 | 2 |
| C2×C61×#360 | 2 |
| #13374 | 61 |