Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. #21461311 | C2 | semidirect |
| 3. #21461242 | C2 | semidirect |
| 5. #21460686 | C2 | semidirect |
| 6. #21460679 | C2 | semidirect |
| 20. #16840167 | C4 | semidirect |
| 21. #16840112 | C4 | semidirect |
| 22. #16840108 | C4 | semidirect |
| 26. C61×#492 | C4 | semidirect |
| 170. #492 | #6923 | semidirect |
| 186. C61 | #9415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462704 | 2 |
| #21461311 | 2 |
| #21461242 | 2 |
| #21461239 | 2 |
| #21460686 | 2 |
| #21460679 | 2 |
| #21456535 | 2 |
| #9415 | 61 |