Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21443802 | C2 | semidirect |
| 5. #21443801 | C2 | semidirect |
| 6. #21443800 | C2 | semidirect |
| 7. C61×#1338 | C2 | semidirect |
| 144. #1338 | D61 | semidirect |
| 168. C61 | #11643 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454750 | 2 |
| #21447621 | 2 |
| #21447620 | 2 |
| #21443802 | 2 |
| #21443801 | 2 |
| #21443800 | 2 |
| C61×#1338 | 2 |
| #11643 | 61 |