Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1220 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1220 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031005 | C2 | semidirect |
| 3. #26019288 | C2 | semidirect |
| 4. #26019220 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. C2×#19151324 | C2 | semidirect |
| 7. C89×#2627 | C2 | semidirect |
| 17. #19151916 | C22 | semidirect |
| 20. #19151737 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151324 | C22 | semidirect |
| 26. #400×C89 | C22 | semidirect |
| 28. #395×C89 | C22 | semidirect |
| 125. C22×C4×C89 | SD16 | semidirect |
| 223. #2627 | D89 | semidirect |
| 228. C89 | #18293 | semidirect |
| 245. #400 | C2×D89 | semidirect |
| 247. #395 | C2×D89 | semidirect |
| 337. C22×C4 | #13083561 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26031005 | 2 |
| #26019288 | 2 |
| #26019220 | 2 |
| #26018819 | 2 |
| C2×#19151324 | 2 |
| C89×#2627 | 2 |
| #18293 | 89 |