Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C2×#16840687 | C2 | semidirect |
| 4. #21460884 | C2 | semidirect |
| 17. C22⋊#11758185 | C4 | semidirect |
| 18. #16839541 | C4 | semidirect |
| 19. C61×C22⋊C16 | C4 | semidirect |
| 44. C2×#11758185 | C2×C4 | semidirect |
| 46. C2×C16×C61 | C2×C4 | semidirect |
| 123. C22×C61 | #365 | semidirect |
| 131. C2×D61 | #365 | semidirect |
| 165. C22⋊C16 | #6923 | semidirect |
| 167. C61 | #12929 | semidirect |
| 187. C2×C16 | C2×#6923 | semidirect |
| 279. C22 | #16840687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519845 | 2 |
| C2×#16840687 | 2 |
| #21461698 | 2 |
| #21460884 | 2 |
| #21447428 | 2 |
| #12929 | 61 |