Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1060 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26031000 | C2 | semidirect |
| 2. C2×#19151732 | C2 | semidirect |
| 3. #26021088 | C2 | semidirect |
| 4. #26020183 | C2 | semidirect |
| 5. #26018820 | C2 | semidirect |
| 6. #26018100 | C2 | semidirect |
| 7. C89×#2433 | C2 | semidirect |
| 31. C22×D356 | D4 | semidirect |
| 37. C22×#10623494 | D4 | semidirect |
| 43. C2×C4⋊Dic89 | D4 | semidirect |
| 55. C22⋊#10623494 | D4 | semidirect |
| 151. C22⋊C4×C89 | D8 | semidirect |
| 271. #2433 | D89 | semidirect |
| 276. C89 | #9946 | semidirect |
| 420. C22⋊C4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031000 | 2 |
| C2×#19151732 | 2 |
| #26021088 | 2 |
| #26020183 | 2 |
| #26018820 | 2 |
| #26018100 | 2 |
| C89×#2433 | 2 |
| #9946 | 89 |