Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21449113 | C2 | semidirect |
| 4. #21443722 | C2 | semidirect |
| 5. #21443721 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 54. C4⋊Q8×C61 | Q8 | semidirect |
| 55. #127×C61 | Q8 | semidirect |
| 222. C61 | #10370 | semidirect |
| 226. C4⋊Q8 | Dic122 | semidirect |
| 227. #127 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21449113 | 2 |
| #21446652 | 2 |
| #21444314 | 2 |
| #21443722 | 2 |
| #21443721 | 2 |
| #21443647 | 2 |
| C61×#1502 | 2 |
| #10370 | 61 |