Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1142 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1142 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 |
|---|---|---|
| 1. C2×#19152224 | C2 | semidirect |
| 2. #26031009 | C2 | semidirect |
| 3. #26019242 | C2 | semidirect |
| 4. #26019174 | C2 | semidirect |
| 5. #26018823 | C2 | semidirect |
| 6. C2×#19151322 | C2 | semidirect |
| 16. #19151928 | C22 | semidirect |
| 19. #19151749 | C22 | semidirect |
| 22. #19151334 | C22 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 42. #15667991 | D4 | semidirect |
| 49. C2×C4⋊Dic89 | D4 | semidirect |
| 111. C24×C89 | SD16 | semidirect |
| 246. C89 | #18286 | semidirect |
| 327. C24 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26031009 | 2 |
| #26019242 | 2 |
| #26019174 | 2 |
| #26018823 | 2 |
| C2×#19151322 | 2 |
| C89×#2617 | 2 |
| #18286 | 89 |