Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
798 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 798 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. #26030811 | C2 | semidirect |
| 2. #26030766 | C2 | semidirect |
| 4. #26019885 | C2 | semidirect |
| 5. #26019880 | C2 | semidirect |
| 6. #26019874 | C2 | semidirect |
| 7. C2×#322×C89 | C2 | semidirect |
| 79. C2×C8×C89 | SD16 | semidirect |
| 127. C2×#322 | D89 | semidirect |
| 128. C89 | #19608 | semidirect |
| 193. C2×C8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030811 | 2 |
| #26030766 | 2 |
| #26030680 | 2 |
| #26019885 | 2 |
| #26019880 | 2 |
| #26019874 | 2 |
| C2×#322×C89 | 2 |
| #19608 | 89 |