Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
878 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 17. #16840142 | C4 | semidirect |
| 18. #16840141 | C4 | semidirect |
| 19. #16840140 | C4 | semidirect |
| 21. C61×#494 | C4 | semidirect |
| 134. #494 | #6923 | semidirect |
| 144. C61 | #23200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462580 | 2 |
| #21461981 | 2 |
| #21461825 | 2 |
| #21461621 | 2 |
| #494×D61 | 2 |
| #23200 | 61 |