Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149725 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C22×D1384 | C2 | semidirect |
| 4. #26012055 | C2 | semidirect |
| 5. #26011638 | C2 | semidirect |
| 6. #26011627 | C2 | semidirect |
| 7. #26011497 | C2 | semidirect |
| 8. #26011488 | C2 | semidirect |
| 9. #408×C173 | C2 | semidirect |
| 14. C2×#14583826 | C22 | semidirect |
| 16. C22×D692 | C22 | semidirect |
| 17. C22×D692 | C22 | semidirect |
| 21. C2×#14583815 | C22 | semidirect |
| 23. C2×D1384 | C22 | semidirect |
| 24. C2×D1384 | C22 | semidirect |
| 27. #19149653 | C22 | semidirect |
| 29. #19149638 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 31. #19149601 | C22 | semidirect |
| 32. #19149601 | C22 | semidirect |
| 34. C2×M16×C173 | C22 | semidirect |
| 35. C22×C8×C173 | C22 | semidirect |
| 36. C22⋊C8×C173 | C22 | semidirect |
| 44. #14583826 | D4 | semidirect |
| 54. C2×D692 | D4 | semidirect |
| 151. C173 | #3008 | semidirect |
| 161. #408 | D173 | semidirect |
| 178. C2×M16 | C2×D173 | semidirect |
| 179. C22×C8 | C2×D173 | semidirect |
| 188. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| C2×#19149707 | 2 |
| C22×D1384 | 2 |
| #26012055 | 2 |
| #26011638 | 2 |
| #26011627 | 2 |
| #26011497 | 2 |
| #26011488 | 2 |
| #408×C173 | 2 |
| #3008 | 173 |