Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 15. #16839893 | C4 | semidirect |
| 17. #16839889 | C4 | semidirect |
| 19. C8×Dic122 | C4 | semidirect |
| 24. C8×Q8×C61 | C4 | semidirect |
| 166. C8×Q8 | #6923 | semidirect |
| 179. C61 | #8677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461369 | 2 |
| #21461252 | 2 |
| #21460674 | 2 |
| #21454748 | 2 |
| #8677 | 61 |