Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023428 | C2 | semidirect |
| 3. #26018965 | C2 | semidirect |
| 4. #26018799 | C2 | semidirect |
| 5. #26018118 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1514 | C2 | semidirect |
| 11. #19151974 | C4 | semidirect |
| 12. #19151972 | C4 | semidirect |
| 45. C4×#10623494 | C2×C4 | semidirect |
| 50. C4⋊Q8×C89 | C2×C4 | semidirect |
| 51. #127×C89 | C2×C4 | semidirect |
| 186. #1514 | D89 | semidirect |
| 189. C89 | #9428 | semidirect |
| 217. C4⋊Q8 | C4×D89 | semidirect |
| 222. #127 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030705 | 2 |
| #26023428 | 2 |
| #26018965 | 2 |
| #26018799 | 2 |
| #26018118 | 2 |
| #26018116 | 2 |
| C89×#1514 | 2 |
| #9428 | 89 |