Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
654 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 116 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. C8×C4⋊#6923 | C2 | semidirect |
| 3. D61⋊#335 | C2 | semidirect |
| 4. D61⋊#331 | C2 | semidirect |
| 18. #16840139 | C4 | semidirect |
| 19. #16840138 | C4 | semidirect |
| 23. C61×#493 | C4 | semidirect |
| 84. C4⋊#6923 | D8 | semidirect |
| 147. C8×C61 | #102 | semidirect |
| 149. #92418 | #102 | semidirect |
| 193. #493 | #6923 | semidirect |
| 204. C61 | #9734 | semidirect |
| 330. C8 | #14519839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461986 | 2 |
| C8×C4⋊#6923 | 2 |
| D61⋊#335 | 2 |
| D61⋊#331 | 2 |
| #493×D61 | 2 |
| #9734 | 61 |