Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
514 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462753 | C2 | semidirect |
| 2. #21461953 | C2 | semidirect |
| 3. C4×#14519842 | C2 | semidirect |
| 4. #21461139 | C2 | semidirect |
| 5. #21460705 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 25. #16840057 | C4 | semidirect |
| 26. #16840053 | C4 | semidirect |
| 27. #16839954 | C4 | semidirect |
| 32. C61×#460 | C4 | semidirect |
| 146. Q8×C61 | #104 | semidirect |
| 229. #460 | #6923 | semidirect |
| 249. C61 | #8970 | semidirect |
| 361. Q8 | #14519841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462753 | 2 |
| #21461953 | 2 |
| C4×#14519842 | 2 |
| #21461139 | 2 |
| #21460705 | 2 |
| #21460646 | 2 |
| #21455878 | 2 |
| #8970 | 61 |