Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21456830 | C2 | semidirect |
| 2. #21455827 | C2 | semidirect |
| 3. #21444456 | C2 | semidirect |
| 4. #21444288 | C2 | semidirect |
| 5. #21444160 | C2 | semidirect |
| 6. #21443680 | C2 | semidirect |
| 231. C61 | #10039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456830 | 2 |
| #21455827 | 2 |
| #21444456 | 2 |
| #21444288 | 2 |
| #21444160 | 2 |
| #21443680 | 2 |
| C61×#3109 | 2 |
| #10039 | 61 |