Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
642 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 112 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. #21461986 | C2 | semidirect |
| 2. #21461613 | C2 | semidirect |
| 3. D61⋊#334 | C2 | semidirect |
| 4. D61⋊#331 | C2 | semidirect |
| 18. #16840139 | C4 | semidirect |
| 19. #16840138 | C4 | semidirect |
| 23. C61×#493 | C4 | semidirect |
| 145. C8×C61 | #102 | semidirect |
| 147. #92418 | #102 | semidirect |
| 190. #493 | #6923 | semidirect |
| 201. C61 | #9743 | semidirect |
| 325. C8 | #14519839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461986 | 2 |
| #21461613 | 2 |
| D61⋊#334 | 2 |
| D61⋊#331 | 2 |
| #493×D61 | 2 |
| #9743 | 61 |