Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26012119 | C2 | semidirect |
| 3. #26011792 | C2 | semidirect |
| 4. #26011792 | C2 | semidirect |
| 5. #26011782 | C2 | semidirect |
| 6. #26011772 | C2 | semidirect |
| 7. #26011533 | C2 | semidirect |
| 8. #26011529 | C2 | semidirect |
| 11. #424×C173 | C2 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 15. #19149671 | C22 | semidirect |
| 26. #19149613 | C22 | semidirect |
| 27. #19149613 | C22 | semidirect |
| 28. #19149613 | C22 | semidirect |
| 29. #19149611 | C22 | semidirect |
| 30. #19149611 | C22 | semidirect |
| 31. #19149611 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 40. C4⋊C8×C173 | C22 | semidirect |
| 45. C2×D692 | Q8 | semidirect |
| 124. C173 | #3081 | semidirect |
| 134. #424 | D173 | semidirect |
| 160. C4⋊C8 | C2×D173 | semidirect |
| 161. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012119 | 2 |
| #26011965 | 2 |
| #26011792 | 2 |
| #26011782 | 2 |
| #26011772 | 2 |
| #26011533 | 2 |
| #26011529 | 2 |
| #26011497 | 2 |
| C2×#19149601 | 2 |
| #424×C173 | 2 |
| #3081 | 173 |