Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
690 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26022849 | C2 | semidirect |
| 3. #26018821 | C2 | semidirect |
| 4. #26018819 | C2 | semidirect |
| 5. C2×#19151321 | C2 | semidirect |
| 6. #26018119 | C2 | semidirect |
| 7. C89×#1289 | C2 | semidirect |
| 12. #19151525 | C4 | semidirect |
| 14. #19151508 | C4 | semidirect |
| 58. #15667919 | D4 | semidirect |
| 68. #95×C89 | D4 | semidirect |
| 257. #1289 | D89 | semidirect |
| 258. C89 | #9205 | semidirect |
| 319. #95 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025989 | 2 |
| #26022849 | 2 |
| #26018821 | 2 |
| #26018819 | 2 |
| C2×#19151321 | 2 |
| #26018119 | 2 |
| C89×#1289 | 2 |
| #9205 | 89 |