Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
514 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 98 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. C8×C4⋊#6923 | C2 | semidirect |
| 2. #21461367 | C2 | semidirect |
| 3. #21461200 | C2 | semidirect |
| 4. #21461199 | C2 | semidirect |
| 5. #21461126 | C2 | semidirect |
| 6. #21461125 | C2 | semidirect |
| 26. #16840141 | C4 | semidirect |
| 27. #16840138 | C4 | semidirect |
| 28. #16840135 | C4 | semidirect |
| 30. C61×#492 | C4 | semidirect |
| 232. #492 | #6923 | semidirect |
| 246. C61 | #9750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C4⋊#6923 | 2 |
| #21461367 | 2 |
| #21461200 | 2 |
| #21461199 | 2 |
| #21461126 | 2 |
| #21461125 | 2 |
| #21456242 | 2 |
| #9750 | 61 |