Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1312 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1312 conjugacy classes of subgroups — too many to draw. Only its 271 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 |
|---|---|---|
| 2. #21454298 | C2 | semidirect |
| 3. #21447510 | C2 | semidirect |
| 4. #21447502 | C2 | semidirect |
| 5. C61×#2888 | C2 | semidirect |
| 17. #16839746 | C22 | semidirect |
| 19. #16839560 | C22 | semidirect |
| 20. #16839558 | C22 | semidirect |
| 23. C61×#413 | C22 | semidirect |
| 181. #2888 | D61 | semidirect |
| 204. #413 | C2×D61 | semidirect |
| 209. C61 | #33373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459593 | 2 |
| #21454298 | 2 |
| #21447510 | 2 |
| #21447502 | 2 |
| C61×#2888 | 2 |
| #33373 | 61 |