Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 96 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×D61⋊M32 | C2 | semidirect |
| 2. C2×#16840679 | C2 | semidirect |
| 3. #21461695 | C2 | semidirect |
| 4. #21460890 | C2 | semidirect |
| 17. #16840000 | C4 | semidirect |
| 18. #16839999 | C4 | semidirect |
| 19. #16839998 | C4 | semidirect |
| 24. C61×#467 | C4 | semidirect |
| 28. #14519852 | D4 | semidirect |
| 167. C2×D61 | #360 | semidirect |
| 198. #467 | #6923 | semidirect |
| 209. C61 | #13065 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊M32 | 2 |
| C2×#16840679 | 2 |
| #21461695 | 2 |
| #21460890 | 2 |
| #21455402 | 2 |
| #13065 | 61 |