Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
306 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 21. C4⋊#11758185 | C4 | semidirect |
| 22. #16839580 | C4 | semidirect |
| 23. #16839580 | C4 | semidirect |
| 24. C61×C4⋊C16 | C4 | semidirect |
| 131. Dic61 | #365 | semidirect |
| 161. C4⋊C16 | #6923 | semidirect |
| 163. C61 | #13185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840687 | 2 |
| C2×#16840686 | 2 |
| #21461759 | 2 |
| C4×#14519845 | 2 |
| #21460884 | 2 |
| #21447573 | 2 |
| #13185 | 61 |