Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
500 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 500 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. #21455937 | C2 | semidirect |
| 2. #21455846 | C2 | semidirect |
| 3. #21444454 | C2 | semidirect |
| 4. #21444288 | C2 | semidirect |
| 5. #21444162 | C2 | semidirect |
| 6. #21443682 | C2 | semidirect |
| 229. C61 | #10040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455937 | 2 |
| #21455846 | 2 |
| #21444454 | 2 |
| #21444288 | 2 |
| #21444162 | 2 |
| #21443682 | 2 |
| C61×#3214 | 2 |
| #10040 | 61 |