Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 106 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. #21461696 | C2 | semidirect |
| 3. #21460682 | C2 | semidirect |
| 10. C22×C8×D61 | C4 | semidirect |
| 15. C2×#14519689 | C4 | semidirect |
| 17. C2×C4×#92418 | C4 | semidirect |
| 18. C2×C4⋊C8×C61 | C4 | semidirect |
| 97. C22×D61 | #107 | semidirect |
| 111. C2×C4×C61 | #107 | semidirect |
| 130. #92418 | #99 | semidirect |
| 175. C2×C4⋊C8 | #6923 | semidirect |
| 183. C61 | #8609 | semidirect |
| 288. C2×C4 | #14519846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461696 | 2 |
| #21461680 | 2 |
| #21460682 | 2 |
| C2×#16839827 | 2 |
| #8609 | 61 |