Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1310 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26029512 | C2 | semidirect |
| 3. #26019208 | C2 | semidirect |
| 4. #26019174 | C2 | semidirect |
| 5. #26018784 | C2 | semidirect |
| 6. #26018579 | C2 | semidirect |
| 18. #19151754 | C22 | semidirect |
| 19. #19151749 | C22 | semidirect |
| 22. #19151334 | C22 | semidirect |
| 33. C22×Dic178 | D4 | semidirect |
| 44. #15667991 | D4 | semidirect |
| 51. C2×C4⋊Dic89 | D4 | semidirect |
| 171. C23×C89 | #137 | semidirect |
| 253. C89 | #18133 | semidirect |
| 417. C23 | #15668042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26029512 | 2 |
| #26019208 | 2 |
| #26019174 | 2 |
| #26018784 | 2 |
| #26018579 | 2 |
| C89×#2404 | 2 |
| #18133 | 89 |