Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21460224 | C2 | semidirect |
| 2. #21457197 | C2 | semidirect |
| 3. #21444962 | C2 | semidirect |
| 4. #21444933 | C2 | semidirect |
| 5. #21444900 | C2 | semidirect |
| 6. #21444871 | C2 | semidirect |
| 7. #21444554 | C2 | semidirect |
| 8. #21444271 | C2 | semidirect |
| 9. C61×#3147 | C2 | semidirect |
| 19. #16840049 | C22 | semidirect |
| 22. #16839954 | C22 | semidirect |
| 23. #16839786 | C22 | semidirect |
| 24. #16839511 | C22 | semidirect |
| 26. #16839491 | C22 | semidirect |
| 27. #16839491 | C22 | semidirect |
| 30. C61×#532 | C22 | semidirect |
| 32. C61×#494 | C22 | semidirect |
| 35. C61×#492 | C22 | semidirect |
| 36. C2×C4×C8×C61 | C22 | semidirect |
| 202. #3147 | D61 | semidirect |
| 225. #532 | C2×D61 | semidirect |
| 227. #494 | C2×D61 | semidirect |
| 230. #492 | C2×D61 | semidirect |
| 237. C2×C4×C8 | C2×D61 | semidirect |
| 242. C61 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460224 | 2 |
| #21457197 | 2 |
| #21444962 | 2 |
| #21444933 | 2 |
| #21444900 | 2 |
| #21444871 | 2 |
| #21444554 | 2 |
| #21444271 | 2 |
| C61×#3147 | 2 |
| #18686 | 61 |