Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26011966 | C2 | semidirect |
| 2. C2×#19149594 | C2 | semidirect |
| 3. C2×#19149594 | C2 | semidirect |
| 4. #26011257 | C2 | semidirect |
| 16. #123×C173 | C4 | semidirect |
| 19. #120×C173 | C4 | semidirect |
| 29. C22⋊Dic173 | D4 | semidirect |
| 31. C24×C173 | C2×C4 | semidirect |
| 44. C22×C4×C173 | C2×C4 | semidirect |
| 50. C22⋊C4×C173 | C2×C4 | semidirect |
| 112. C173 | #1913 | semidirect |
| 122. #123 | Dic173 | semidirect |
| 125. #120 | Dic173 | semidirect |
| 134. C24 | C2×Dic173 | semidirect |
| 150. C22×C4 | C2×Dic173 | semidirect |
| 162. C22⋊C4 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011966 | 2 |
| C2×#19149594 | 2 |
| #26011257 | 2 |
| #534×C173 | 2 |
| #1913 | 173 |