Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1354 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 254 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. Q8×C22⋊#6923 | C2 | semidirect |
| 2. #21462008 | C2 | semidirect |
| 17. C2×#14519775 | C4 | semidirect |
| 18. C2×#14519756 | C4 | semidirect |
| 20. C2×Q8×Dic61 | C4 | semidirect |
| 22. C23×Q8×C61 | C4 | semidirect |
| 29. #14519835 | Q8 | direct (N × H) |
| 95. C22⋊#6923 | C2×Q8 | semidirect |
| 110. C23×C61 | C4×Q8 | semidirect |
| 127. Q8×C61 | #99 | semidirect |
| 143. C2×Dic61 | C4×Q8 | semidirect |
| 188. C23×Q8 | #6923 | semidirect |
| 204. C61 | Q8×#99 | semidirect |
| 298. C23 | Q8×#6923 | semidirect |
| 305. Q8 | #14519835 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊#6923 | 2 |
| #21462008 | 2 |
| #21461679 | 2 |
| C4×#14519835 | 2 |
| C2×Q8×C22⋊D61 | 2 |
| Q8×#99 | 61 |