Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#19149706 | C2 | semidirect |
| 2. #26012042 | C2 | semidirect |
| 3. C4×D4×D173 | C2 | semidirect |
| 4. #26011709 | C2 | semidirect |
| 5. #26011708 | C2 | semidirect |
| 6. #26011693 | C2 | semidirect |
| 7. #26011687 | C2 | semidirect |
| 8. #26011686 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 10. #26011491 | C2 | semidirect |
| 11. #461×C173 | C2 | semidirect |
| 20. #19149676 | C22 | semidirect |
| 21. #19149668 | C22 | semidirect |
| 34. C4⋊#13063436 | C22 | semidirect |
| 35. #19149608 | C22 | semidirect |
| 36. #19149603 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 38. #19149599 | C22 | semidirect |
| 40. C4⋊Q8×C173 | C22 | semidirect |
| 42. C4⋊C8×C173 | C22 | semidirect |
| 43. #103×C173 | C22 | semidirect |
| 54. D4×D173 | D4 | semidirect |
| 146. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 160. C173 | #3036 | semidirect |
| 168. #461 | D173 | semidirect |
| 182. C4⋊Q8 | C2×D173 | semidirect |
| 200. C4⋊C8 | C2×D173 | semidirect |
| 202. #103 | C2×D173 | semidirect |
| 311. C4 | #19149706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149706 | 2 |
| #26012042 | 2 |
| C4×D4×D173 | 2 |
| #26011709 | 2 |
| #26011708 | 2 |
| #26011693 | 2 |
| #26011687 | 2 |
| #26011686 | 2 |
| #26011513 | 2 |
| #26011491 | 2 |
| #461×C173 | 2 |
| #3036 | 173 |