Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
430 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21446768 | C2 | semidirect |
| 5. #21443688 | C2 | semidirect |
| 6. #21443676 | C2 | semidirect |
| 7. C61×#1556 | C2 | semidirect |
| 9. #16840154 | C4 | semidirect |
| 10. #16840130 | C4 | semidirect |
| 187. #1556 | D61 | semidirect |
| 222. C61 | #9376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456846 | 2 |
| #21454960 | 2 |
| #21446768 | 2 |
| #21444345 | 2 |
| #21443688 | 2 |
| #21443676 | 2 |
| C61×#1556 | 2 |
| #9376 | 61 |