Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1022 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 191 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. #21459629 | C2 | semidirect |
| 3. #21446975 | C2 | semidirect |
| 4. #21446762 | C2 | semidirect |
| 5. #21446223 | C2 | semidirect |
| 6. C4×#14519696 | C2 | semidirect |
| 212. C61 | #25920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459629 | 2 |
| #21456193 | 2 |
| #21446975 | 2 |
| #21446762 | 2 |
| #21446223 | 2 |
| C4×#14519696 | 2 |
| C61×#2548 | 2 |
| #25920 | 61 |