Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
906 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 227 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. #26030831 | C2 | semidirect |
| 2. #26030680 | C2 | semidirect |
| 3. #26019923 | C2 | semidirect |
| 4. #26019918 | C2 | semidirect |
| 5. C2×#322×C89 | C2 | semidirect |
| 55. C2×C8×C89 | D8 | semidirect |
| 96. C2×#322 | D89 | semidirect |
| 97. C89 | #19616 | semidirect |
| 145. C2×C8 | D712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030831 | 2 |
| #26030680 | 2 |
| #26019923 | 2 |
| #26019918 | 2 |
| C2×#322×C89 | 2 |
| #19616 | 89 |