Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
592 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #21457131 | C2 | semidirect |
| 3. #21456195 | C2 | semidirect |
| 4. #21446746 | C2 | semidirect |
| 5. #21446737 | C2 | semidirect |
| 6. #21443668 | C2 | semidirect |
| 7. C61×#1503 | C2 | semidirect |
| 205. #1503 | D61 | semidirect |
| 237. C61 | #10193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457131 | 2 |
| #21456739 | 2 |
| #21456195 | 2 |
| #21446746 | 2 |
| #21446737 | 2 |
| #21443668 | 2 |
| C61×#1503 | 2 |
| #10193 | 61 |