Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
352 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21447622 | C2 | semidirect |
| 3. #21443830 | C2 | semidirect |
| 5. C4×#107×C61 | C2 | semidirect |
| 7. #16840164 | C4 | semidirect |
| 8. #16840146 | C4 | semidirect |
| 13. C4×Dic244 | C4 | semidirect |
| 15. C4×D488 | C4 | semidirect |
| 144. C4×#107 | D61 | semidirect |
| 170. C61 | #11746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456389 | 2 |
| #21447622 | 2 |
| #21443830 | 2 |
| #21443827 | 2 |
| C4×#107×C61 | 2 |
| #11746 | 61 |