Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1190 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 271 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. #26028716 | C2 | semidirect |
| 3. #26021907 | C2 | semidirect |
| 4. #26021894 | C2 | semidirect |
| 5. C89×#2889 | C2 | semidirect |
| 6. C22×Q8×D89 | C4 | semidirect |
| 11. #19152169 | C4 | semidirect |
| 13. #19152105 | C4 | semidirect |
| 16. #19152076 | C4 | semidirect |
| 182. #2889 | D89 | semidirect |
| 186. C89 | #33349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033900 | 2 |
| #26028716 | 2 |
| #26021907 | 2 |
| #26021894 | 2 |
| C89×#2889 | 2 |
| #33349 | 89 |