Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26021170 | C2 | semidirect |
| 3. #26018759 | C2 | semidirect |
| 4. #26018695 | C2 | semidirect |
| 5. #26018145 | C2 | semidirect |
| 6. #26018108 | C2 | semidirect |
| 7. C89×#2275 | C2 | semidirect |
| 10. #19151888 | C4 | semidirect |
| 11. #19151793 | C4 | semidirect |
| 32. #15668012 | C2×C4 | semidirect |
| 33. #15668009 | C2×C4 | semidirect |
| 41. C4⋊#10623494 | C2×C4 | semidirect |
| 129. D4×C89 | #104 | semidirect |
| 198. #2275 | D89 | semidirect |
| 204. C89 | #9325 | semidirect |
| 332. D4 | #15667940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030343 | 2 |
| #26021170 | 2 |
| #26018759 | 2 |
| #26018695 | 2 |
| #26018145 | 2 |
| #26018108 | 2 |
| C89×#2275 | 2 |
| #9325 | 89 |