Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
596 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. #26020001 | C2 | semidirect |
| 3. C2×#19151337 | C2 | semidirect |
| 4. C89×#1767 | C2 | semidirect |
| 38. #15667923 | D4 | semidirect |
| 163. #1767 | D89 | semidirect |
| 166. C89 | #9689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028609 | 2 |
| #26020001 | 2 |
| C2×#19151337 | 2 |
| C89×#1767 | 2 |
| #9689 | 89 |