Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21454842 | C2 | semidirect |
| 3. #21445808 | C2 | semidirect |
| 4. #21444488 | C2 | semidirect |
| 5. #21444486 | C2 | semidirect |
| 6. #21443722 | C2 | semidirect |
| 7. C61×#1303 | C2 | semidirect |
| 50. C4⋊#92418 | D4 | semidirect |
| 61. C4⋊C8×C61 | D4 | semidirect |
| 196. #1303 | D61 | semidirect |
| 222. C61 | #9397 | semidirect |
| 254. C4⋊C8 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454842 | 2 |
| #21450761 | 2 |
| #21445808 | 2 |
| #21444488 | 2 |
| #21444486 | 2 |
| #21443722 | 2 |
| C61×#1303 | 2 |
| #9397 | 61 |