Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1412 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 240 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. #21461959 | C2 | semidirect |
| 3. #21461680 | C2 | semidirect |
| 4. C4×#14519836 | C2 | semidirect |
| 14. C22×#11758226 | C4 | semidirect |
| 18. C2×#14519765 | C4 | semidirect |
| 19. C2×#14519757 | C4 | semidirect |
| 22. C2×C4×Q8×C61 | C4 | semidirect |
| 95. C22⋊#6923 | #41 | semidirect |
| 125. Q8×C61 | #99 | semidirect |
| 195. C2×C4×Q8 | #6923 | semidirect |
| 204. C61 | #22534 | semidirect |
| 303. Q8 | #14519836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊#6923 | 2 |
| #21461959 | 2 |
| #21461680 | 2 |
| C4×#14519836 | 2 |
| C2×#16840424 | 2 |
| #22534 | 61 |