Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21444602 | C2 | semidirect |
| 4. #21444318 | C2 | semidirect |
| 6. #21443674 | C2 | semidirect |
| 7. C61×#1552 | C2 | semidirect |
| 181. #1552 | D61 | semidirect |
| 212. C61 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456818 | 2 |
| #21446749 | 2 |
| #21444602 | 2 |
| #21444318 | 2 |
| #21444172 | 2 |
| #21443674 | 2 |
| C61×#1552 | 2 |
| #10510 | 61 |