Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
526 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19151391 | C2 | semidirect |
| 3. #26018414 | C2 | direct (N × H) |
| 4. C2×#353×C89 | C2 | semidirect |
| 7. C2×#15668009 | C4 | semidirect |
| 10. #19151974 | C4 | semidirect |
| 13. C2×C4×#10623494 | C4 | semidirect |
| 15. #19151391 | C22 | semidirect |
| 19. #353×C89 | C22 | semidirect |
| 33. #15668009 | C2×C4 | semidirect |
| 38. C4×#10623494 | C2×C4 | semidirect |
| 172. C2×C89 | #1408 | semidirect |
| 177. C2×#353 | D89 | semidirect |
| 179. C89 | C2×#1408 | semidirect |
| 194. #353 | C2×D89 | semidirect |
| 347. C2 | #26018414 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151974 | 2 |
| C2×#19151391 | 2 |
| #26018414 | 2 |
| C2×#353×C89 | 2 |
| C2×#1408 | 89 |