Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
850 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 124 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. #21461735 | C2 | semidirect |
| 2. #21461604 | C2 | semidirect |
| 3. C2×#16840620 | C2 | semidirect |
| 25. #14519844 | D4 | semidirect |
| 222. C61 | #9706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461735 | 2 |
| #21461604 | 2 |
| C2×#16840620 | 2 |
| #21454213 | 2 |
| #9706 | 61 |