Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 11. Q16×#6923 | C4 | semidirect |
| 17. #16840675 | C4 | semidirect |
| 23. #16839567 | C4 | semidirect |
| 24. #16839566 | C4 | semidirect |
| 25. #16839565 | C4 | semidirect |
| 26. C61×#358 | C4 | semidirect |
| 91. Q16×C61 | C42 | semidirect |
| 100. Dic244 | C42 | semidirect |
| 196. #358 | #6923 | semidirect |
| 199. C61 | #12638 | semidirect |
| 256. Q16 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×#6923 | 2 |
| C2×#16840675 | 2 |
| C2×#16840649 | 2 |
| #107×#6923 | 2 |
| #21460877 | 2 |
| #21460876 | 2 |
| #358×D61 | 2 |
| #12638 | 61 |