Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
364 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 364 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 |
|---|---|---|
| 3. #21443772 | C2 | semidirect |
| 4. #21443771 | C2 | semidirect |
| 5. C61×#1328 | C2 | semidirect |
| 125. #1328 | D61 | semidirect |
| 144. C61 | #11458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454380 | 2 |
| #349×D61 | 2 |
| #21443772 | 2 |
| #21443771 | 2 |
| C61×#1328 | 2 |
| #11458 | 61 |