Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #21454914 | C2 | semidirect |
| 5. #21443689 | C2 | semidirect |
| 6. #21443682 | C2 | semidirect |
| 7. C61×#1552 | C2 | semidirect |
| 157. #1552 | D61 | semidirect |
| 188. C61 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457017 | 2 |
| #21454914 | 2 |
| #21444453 | 2 |
| #21444217 | 2 |
| #21443689 | 2 |
| #21443682 | 2 |
| C61×#1552 | 2 |
| #9372 | 61 |