Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
586 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 586 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. #21461998 | C2 | semidirect |
| 3. C8×C4⋊#6923 | C2 | semidirect |
| 4. D61⋊#334 | C2 | semidirect |
| 5. D61⋊#332 | C2 | semidirect |
| 24. #16840136 | C4 | semidirect |
| 25. #16840135 | C4 | semidirect |
| 26. #16840134 | C4 | semidirect |
| 30. C61×#492 | C4 | semidirect |
| 113. C4⋊#6923 | SD16 | semidirect |
| 196. C8×C61 | #102 | semidirect |
| 198. #92418 | #102 | semidirect |
| 248. #492 | #6923 | semidirect |
| 262. C61 | #9732 | semidirect |
| 430. C8 | #14519839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461998 | 2 |
| #21461986 | 2 |
| C8×C4⋊#6923 | 2 |
| D61⋊#334 | 2 |
| D61⋊#332 | 2 |
| D61⋊#331 | 2 |
| #492×D61 | 2 |
| #9732 | 61 |