Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012096 | C2 | semidirect |
| 2. #26011965 | C2 | semidirect |
| 3. #26011816 | C2 | semidirect |
| 4. #26011792 | C2 | semidirect |
| 5. #26011687 | C2 | semidirect |
| 6. #26011627 | C2 | semidirect |
| 7. #26011604 | C2 | semidirect |
| 8. C4×D1384 | C2 | semidirect |
| 9. #433×C173 | C2 | semidirect |
| 13. #19149676 | C22 | semidirect |
| 14. #19149671 | C22 | semidirect |
| 20. C4×D692 | C22 | semidirect |
| 24. #19149613 | C22 | semidirect |
| 25. #19149611 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 31. C4⋊C8×C173 | C22 | semidirect |
| 33. #97×C173 | C22 | semidirect |
| 34. C4×C8×C173 | C22 | semidirect |
| 108. C173 | #3122 | semidirect |
| 118. #433 | D173 | semidirect |
| 136. C4⋊C8 | C2×D173 | semidirect |
| 142. #97 | C2×D173 | semidirect |
| 143. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012096 | 2 |
| #26011965 | 2 |
| #26011816 | 2 |
| #26011792 | 2 |
| #26011687 | 2 |
| #26011627 | 2 |
| #26011604 | 2 |
| C4×D1384 | 2 |
| #433×C173 | 2 |
| #3122 | 173 |