Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21447593 | C2 | semidirect |
| 4. #21446565 | C2 | semidirect |
| 5. #21443921 | C2 | semidirect |
| 6. #21443900 | C2 | semidirect |
| 19. #16839572 | C4 | semidirect |
| 36. #14519717 | C2×C4 | semidirect |
| 40. #14519709 | C2×C4 | semidirect |
| 180. C61 | #12951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×Dic61 | 2 |
| #21447593 | 2 |
| #21447555 | 2 |
| #21446565 | 2 |
| #21443921 | 2 |
| #21443900 | 2 |
| C61×#2148 | 2 |
| #12951 | 61 |