Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21456359 | C2 | semidirect |
| 4. #21443928 | C2 | semidirect |
| 5. #21443914 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 54. C2×D8×C61 | Q8 | semidirect |
| 183. C61 | #13369 | semidirect |
| 190. C2×D8 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456359 | 2 |
| C2×#16839563 | 2 |
| #21446730 | 2 |
| #21443928 | 2 |
| #21443914 | 2 |
| #21443909 | 2 |
| C61×#2140 | 2 |
| #13369 | 61 |