Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
682 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021656 | C2 | semidirect |
| 3. #26018073 | C2 | semidirect |
| 4. #26018072 | C2 | semidirect |
| 5. C89×#2093 | C2 | semidirect |
| 13. #19151353 | C22 | semidirect |
| 17. #384×C89 | C22 | semidirect |
| 18. #336×C89 | C22 | semidirect |
| 165. #2093 | D89 | semidirect |
| 169. C89 | #7786 | semidirect |
| 179. #384 | C2×D89 | semidirect |
| 182. #336 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026587 | 2 |
| #26021656 | 2 |
| #26018073 | 2 |
| #26018072 | 2 |
| C89×#2093 | 2 |
| #7786 | 89 |