Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
828 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19151790 | C2 | semidirect |
| 2. #26025168 | C2 | semidirect |
| 3. C2×#19151327 | C2 | semidirect |
| 4. #26018135 | C2 | semidirect |
| 5. C89×#1957 | C2 | semidirect |
| 37. C4⋊#10623494 | D4 | semidirect |
| 45. #127×C89 | D4 | semidirect |
| 59. C2×D356 | D8 | semidirect |
| 179. #1957 | D89 | semidirect |
| 182. C89 | #10228 | semidirect |
| 209. #127 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151790 | 2 |
| #26025168 | 2 |
| C2×#19151327 | 2 |
| #26018135 | 2 |
| C89×#1957 | 2 |
| #10228 | 89 |