Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21444556 | C2 | semidirect |
| 5. #21444239 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1574 | C2 | semidirect |
| 162. #1574 | D61 | semidirect |
| 191. C61 | #10492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456762 | 2 |
| #21446658 | 2 |
| #21444556 | 2 |
| #21444486 | 2 |
| #21444239 | 2 |
| #21443710 | 2 |
| C61×#1574 | 2 |
| #10492 | 61 |