Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
488 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21446640 | C2 | semidirect |
| 4. #21444383 | C2 | semidirect |
| 6. #21443663 | C2 | semidirect |
| 7. C61×#3229 | C2 | semidirect |
| 176. #3229 | D61 | semidirect |
| 212. C61 | #10226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456940 | 2 |
| #21456167 | 2 |
| #21446640 | 2 |
| #21444383 | 2 |
| #21444380 | 2 |
| #21443663 | 2 |
| C61×#3229 | 2 |
| #10226 | 61 |