Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 3. #21445622 | C2 | semidirect |
| 4. #21443949 | C2 | semidirect |
| 6. C2×#14519784 | C4 | semidirect |
| 10. #16839786 | C4 | semidirect |
| 12. #16839729 | C4 | semidirect |
| 15. C2×#14519688 | C4 | semidirect |
| 21. C61×#356 | C4 | semidirect |
| 22. C61×#355 | C4 | semidirect |
| 164. #356 | Dic61 | semidirect |
| 165. #355 | Dic61 | semidirect |
| 169. C61 | #12634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454537 | 2 |
| #21447484 | 2 |
| #21445622 | 2 |
| #21443949 | 2 |
| C61×#2132 | 2 |
| #12634 | 61 |