Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19149596 | C2 | semidirect |
| 2. C2×#19149594 | C2 | semidirect |
| 3. #26011281 | C2 | semidirect |
| 4. #26011278 | C2 | semidirect |
| 12. C22×D4×C173 | C4 | semidirect |
| 15. #123×C173 | C4 | semidirect |
| 20. #120×C173 | C4 | semidirect |
| 22. C2×C22⋊C4×C173 | C4 | semidirect |
| 30. C24×C173 | C2×C4 | semidirect |
| 45. C22×C4×C173 | C2×C4 | semidirect |
| 54. C22⋊C4×C173 | C2×C4 | semidirect |
| 55. C22⋊C4×C173 | C2×C4 | semidirect |
| 126. C173 | #2121 | semidirect |
| 133. C22×D4 | Dic173 | semidirect |
| 137. #123 | Dic173 | semidirect |
| 142. #120 | Dic173 | semidirect |
| 145. C2×C22⋊C4 | Dic173 | semidirect |
| 151. C24 | C2×Dic173 | semidirect |
| 167. C22×C4 | C2×Dic173 | semidirect |
| 181. C22⋊C4 | C2×Dic173 | semidirect |
| 182. C22⋊C4 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149596 | 2 |
| C2×#19149594 | 2 |
| #26011281 | 2 |
| #26011278 | 2 |
| #534×C173 | 2 |
| #2121 | 173 |