Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
780 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#19151985 | C2 | semidirect |
| 2. #26028298 | C2 | semidirect |
| 3. C2×#19151337 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 5. C89×#1961 | C2 | semidirect |
| 36. #15667923 | D4 | semidirect |
| 43. #127×C89 | D4 | semidirect |
| 148. #1961 | D89 | semidirect |
| 151. C89 | #10078 | semidirect |
| 179. #127 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151985 | 2 |
| #26028298 | 2 |
| C2×#19151337 | 2 |
| #26018133 | 2 |
| C89×#1961 | 2 |
| #10078 | 89 |