Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 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. #21460233 | C2 | semidirect |
| 2. #21456760 | C2 | semidirect |
| 3. #21444895 | C2 | semidirect |
| 4. #21444876 | C2 | semidirect |
| 5. #21444481 | C2 | semidirect |
| 6. #21444241 | C2 | semidirect |
| 9. #16840498 | C22 | semidirect |
| 10. #16840492 | C22 | semidirect |
| 21. #16839511 | C22 | semidirect |
| 22. #16839506 | C22 | semidirect |
| 23. #16839494 | C22 | semidirect |
| 198. C61 | #18718 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460233 | 2 |
| #21456760 | 2 |
| #21444895 | 2 |
| #21444876 | 2 |
| #21444481 | 2 |
| #21444241 | 2 |
| C61×#3151 | 2 |
| #18718 | 61 |