Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1434 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 275 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. #26021428 | C2 | direct (N × H) |
| 3. C2×#19151364 | C2 | semidirect |
| 4. C2×#543×C89 | C2 | semidirect |
| 10. #19151364 | C22 | semidirect |
| 12. #543×C89 | C22 | semidirect |
| 15. C24×D89 | Q8 | semidirect |
| 20. C22×C22⋊D89 | Q8 | semidirect |
| 23. C23×Dic89 | Q8 | semidirect |
| 46. C23×D89 | C2×Q8 | semidirect |
| 63. C22×Dic89 | C2×Q8 | semidirect |
| 163. C2×C89 | #2032 | semidirect |
| 166. C2×#543 | D89 | semidirect |
| 170. C89 | C2×#2032 | semidirect |
| 173. #543 | C2×D89 | semidirect |
| 329. C2 | #26021428 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667926 | 2 |
| #26021428 | 2 |
| C2×#19151364 | 2 |
| C2×#543×C89 | 2 |
| C2×#2032 | 89 |