Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #99×Dic89 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 6. C2×D4×Dic89 | C4 | semidirect |
| 9. #19151501 | C4 | semidirect |
| 13. #19151464 | C4 | semidirect |
| 15. #19151444 | C4 | semidirect |
| 16. #19151391 | C4 | semidirect |
| 20. #353×C89 | C4 | semidirect |
| 36. #15667927 | C2×C4 | semidirect |
| 50. #99×C89 | C2×C4 | semidirect |
| 84. C2×D4×C89 | C42 | semidirect |
| 94. C42×C89 | C42 | semidirect |
| 182. C89 | #12628 | semidirect |
| 196. #353 | Dic89 | semidirect |
| 223. #99 | C2×Dic89 | semidirect |
| 239. C2×D4 | C4×Dic89 | semidirect |
| 271. C42 | C4×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022978 | 2 |
| C2×#19151391 | 2 |
| #99×Dic89 | 2 |
| #26018376 | 2 |
| C2×#353×C89 | 2 |
| #12628 | 89 |