Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
802 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 802 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. #26021087 | C2 | semidirect |
| 3. #26020196 | C2 | semidirect |
| 4. #26018767 | C2 | semidirect |
| 5. #26018158 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#2339 | C2 | semidirect |
| 8. C2×#15668037 | C4 | semidirect |
| 14. #19151599 | C4 | semidirect |
| 29. C22×D356 | C2×C4 | semidirect |
| 35. C2×#13083558 | C2×C4 | semidirect |
| 40. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 160. D4×C89 | #99 | semidirect |
| 240. #2339 | D89 | semidirect |
| 246. C89 | #9365 | semidirect |
| 404. D4 | #15667926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029504 | 2 |
| #26021087 | 2 |
| #26020196 | 2 |
| #26018767 | 2 |
| #26018158 | 2 |
| #26018138 | 2 |
| C89×#2339 | 2 |
| #9365 | 89 |