Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21444608 | C2 | semidirect |
| 4. #21444607 | C2 | semidirect |
| 6. #21443652 | C2 | semidirect |
| 7. C61×#1276 | C2 | semidirect |
| 22. #16839510 | C4 | semidirect |
| 23. #16839510 | C4 | semidirect |
| 24. #16839505 | C4 | semidirect |
| 25. #16839505 | C4 | semidirect |
| 164. #1276 | D61 | semidirect |
| 191. C61 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454885 | 2 |
| #21446647 | 2 |
| #21444608 | 2 |
| #21444607 | 2 |
| #21444479 | 2 |
| #21443652 | 2 |
| C61×#1276 | 2 |
| #8934 | 61 |