Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
434 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 1. #21461756 | C2 | semidirect |
| 2. #21461367 | C2 | semidirect |
| 4. #21460674 | C2 | semidirect |
| 16. #16839841 | C4 | semidirect |
| 18. D4×#92418 | C4 | semidirect |
| 19. #16839827 | C4 | semidirect |
| 24. C61×#436 | C4 | semidirect |
| 192. #436 | #6923 | semidirect |
| 207. C61 | #8676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461367 | 2 |
| #21461249 | 2 |
| #21460674 | 2 |
| #21454528 | 2 |
| #8676 | 61 |