Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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. D61⋊#368 | C2 | semidirect |
| 2. C2×#16840688 | C2 | semidirect |
| 4. #21460894 | C2 | semidirect |
| 16. #16840180 | C4 | semidirect |
| 17. #16840179 | C4 | semidirect |
| 19. #16840178 | C4 | semidirect |
| 24. C61×#504 | C4 | semidirect |
| 170. #504 | #6923 | semidirect |
| 183. C61 | #12842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#368 | 2 |
| C2×#16840688 | 2 |
| #21461708 | 2 |
| #21460894 | 2 |
| #504×D61 | 2 |
| #12842 | 61 |