Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
600 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 106 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. #21461545 | C2 | semidirect |
| 2. C2×#16840628 | C2 | semidirect |
| 3. #21460640 | C2 | semidirect |
| 4. #21460635 | C2 | semidirect |
| 223. C61 | #7690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461545 | 2 |
| C2×#16840628 | 2 |
| #21460640 | 2 |
| #21460635 | 2 |
| #21454118 | 2 |
| #7690 | 61 |