Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21454195 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443651 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 25. #14519777 | Q8 | semidirect |
| 28. #14519774 | Q8 | semidirect |
| 170. #1286 | D61 | semidirect |
| 193. C61 | #10362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454195 | 2 |
| #21446646 | 2 |
| #21444380 | 2 |
| #21444378 | 2 |
| #21443679 | 2 |
| #21443651 | 2 |
| C61×#1286 | 2 |
| #10362 | 61 |