Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
594 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 92 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. #21461959 | C2 | semidirect |
| 2. #21461695 | C2 | semidirect |
| 3. #21461555 | C2 | semidirect |
| 4. #21461256 | C2 | semidirect |
| 15. C22×D488 | C4 | semidirect |
| 22. C2×#14519697 | C4 | semidirect |
| 23. C2×#107×C61 | C4 | semidirect |
| 144. C8×C61 | #99 | semidirect |
| 190. C2×#107 | #6923 | semidirect |
| 201. C61 | #9785 | semidirect |
| 324. C8 | #14519836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461959 | 2 |
| #21461695 | 2 |
| #21461555 | 2 |
| #21461256 | 2 |
| C2×#16839999 | 2 |
| #9785 | 61 |