Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. #21445991 | C2 | semidirect |
| 3. #21444557 | C2 | semidirect |
| 6. #21443732 | C2 | semidirect |
| 7. C61×#1493 | C2 | semidirect |
| 164. #1493 | D61 | semidirect |
| 191. C61 | #10532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457202 | 2 |
| #21445991 | 2 |
| #21444557 | 2 |
| #21444552 | 2 |
| #21444271 | 2 |
| #21443732 | 2 |
| C61×#1493 | 2 |
| #10532 | 61 |