Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26012048 | C2 | semidirect |
| 3. #26011792 | C2 | semidirect |
| 4. #26011782 | C2 | semidirect |
| 5. #26011772 | C2 | semidirect |
| 6. #26011533 | C2 | semidirect |
| 8. #423×C173 | C2 | semidirect |
| 11. #19149679 | C22 | semidirect |
| 12. #19149679 | C22 | semidirect |
| 13. #19149671 | C22 | semidirect |
| 25. #19149613 | C22 | semidirect |
| 26. #19149611 | C22 | semidirect |
| 31. C4⋊C8×C173 | C22 | semidirect |
| 32. C4⋊C8×C173 | C22 | semidirect |
| 38. C2×D692 | Q8 | semidirect |
| 115. C173 | #3077 | semidirect |
| 123. #423 | D173 | semidirect |
| 145. C4⋊C8 | C2×D173 | semidirect |
| 146. C4⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×C4×D692 | 2 |
| #26011792 | 2 |
| #26011782 | 2 |
| #26011772 | 2 |
| #26011533 | 2 |
| #26011497 | 2 |
| #423×C173 | 2 |
| #3077 | 173 |