Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
514 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. C4×#14519831 | C2 | semidirect |
| 4. #21461031 | C2 | semidirect |
| 5. #21460651 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 8. Q8×#92420 | C4 | semidirect |
| 10. #16840790 | C4 | semidirect |
| 25. Q8⋊#92418 | C4 | semidirect |
| 26. #16839491 | C4 | semidirect |
| 27. #16839489 | C4 | semidirect |
| 28. C61×Q8⋊C8 | C4 | semidirect |
| 117. Q8×C61 | #97 | semidirect |
| 129. D244 | #97 | semidirect |
| 142. #92420 | #104 | semidirect |
| 195. Q8⋊C8 | #6923 | semidirect |
| 200. C61 | #8192 | semidirect |
| 286. Q8 | #14519831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462625 | 2 |
| C4×#14519842 | 2 |
| C4×#14519831 | 2 |
| #21461031 | 2 |
| #21460651 | 2 |
| #21460646 | 2 |
| #21444200 | 2 |
| #8192 | 61 |