Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
850 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 850 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26031049 | C2 | semidirect |
| 2. #26029504 | C2 | semidirect |
| 3. #26021087 | C2 | semidirect |
| 4. #26020196 | C2 | semidirect |
| 5. #26018768 | C2 | semidirect |
| 6. #26018158 | C2 | semidirect |
| 7. C89×#2615 | C2 | semidirect |
| 33. C22×D356 | D4 | semidirect |
| 40. C2×#13083558 | D4 | semidirect |
| 45. C2×C4⋊Dic89 | D4 | semidirect |
| 59. C22⋊#10623494 | D4 | semidirect |
| 284. #2615 | D89 | semidirect |
| 289. C89 | #9930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26029504 | 2 |
| #26021087 | 2 |
| #26020196 | 2 |
| #26018768 | 2 |
| #26018158 | 2 |
| C89×#2615 | 2 |
| #9930 | 89 |