Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1394 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1394 conjugacy classes of subgroups — too many to draw. Only its 224 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. #21462266 | C2 | semidirect |
| 2. #21461959 | C2 | semidirect |
| 3. #21461650 | C2 | semidirect |
| 18. C2×#14519774 | C4 | semidirect |
| 19. C2×#14519766 | C4 | semidirect |
| 21. C2×#14519739 | C4 | semidirect |
| 23. C2×C4⋊Q8×C61 | C4 | semidirect |
| 187. C2×C4⋊Q8 | #6923 | semidirect |
| 201. C61 | #21794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462266 | 2 |
| #21461959 | 2 |
| #21461650 | 2 |
| C2×#16840313 | 2 |
| #21794 | 61 |