Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
626 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 132 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. #21462000 | C2 | semidirect |
| 3. #21461755 | C2 | semidirect |
| 4. #21461013 | C2 | semidirect |
| 15. #16840136 | C4 | semidirect |
| 16. #16840135 | C4 | semidirect |
| 17. #16840134 | C4 | semidirect |
| 20. C61×#492 | C4 | semidirect |
| 124. C8×C61 | #102 | semidirect |
| 125. #92418 | #102 | semidirect |
| 165. #492 | #6923 | semidirect |
| 173. C61 | #9842 | semidirect |
| 278. C8 | #14519839 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462000 | 2 |
| #21461947 | 2 |
| #21461755 | 2 |
| #21461013 | 2 |
| #492×D61 | 2 |
| #9842 | 61 |