Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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. #21446797 | C2 | semidirect |
| 4. C4×C8×Dic61 | C2 | semidirect |
| 5. #21444574 | C2 | semidirect |
| 7. C61×#1493 | C2 | semidirect |
| 9. #16840158 | C4 | semidirect |
| 10. #16840136 | C4 | semidirect |
| 11. #16840112 | C4 | semidirect |
| 12. #16840110 | C4 | semidirect |
| 104. C4×Dic61 | SD16 | semidirect |
| 141. #92418 | #104 | semidirect |
| 166. #1493 | D61 | semidirect |
| 192. C61 | #9843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456379 | 2 |
| #21446797 | 2 |
| #21446646 | 2 |
| C4×C8×Dic61 | 2 |
| #21444574 | 2 |
| #21444271 | 2 |
| C61×#1493 | 2 |
| #9843 | 61 |