Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
684 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21456824 | C2 | semidirect |
| 2. #21456193 | C2 | semidirect |
| 4. #21444418 | C2 | semidirect |
| 5. #21444332 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 7. C61×#1555 | C2 | semidirect |
| 37. #14519777 | D4 | semidirect |
| 38. #14519777 | D4 | semidirect |
| 59. #14519688 | D4 | semidirect |
| 72. C4⋊C8×C61 | D4 | semidirect |
| 198. #1555 | D61 | semidirect |
| 231. C61 | #10096 | semidirect |
| 265. C4⋊C8 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456824 | 2 |
| #21456193 | 2 |
| #21451926 | 2 |
| #21444418 | 2 |
| #21444332 | 2 |
| #21443711 | 2 |
| C61×#1555 | 2 |
| #10096 | 61 |