Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 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. #21444456 | C2 | semidirect |
| 5. #21444221 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 7. C61×#1290 | C2 | semidirect |
| 164. #1290 | D61 | semidirect |
| 192. C61 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456832 | 2 |
| #21454897 | 2 |
| #21444512 | 2 |
| #21444456 | 2 |
| #21444221 | 2 |
| #21443680 | 2 |
| C61×#1290 | 2 |
| #9373 | 61 |