Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012025 | C2 | semidirect |
| 2. C2×C4×D692 | C2 | semidirect |
| 3. #26011822 | C2 | semidirect |
| 4. #26011805 | C2 | semidirect |
| 5. #26011792 | C2 | semidirect |
| 6. #26011707 | C2 | semidirect |
| 7. #26011644 | C2 | semidirect |
| 9. #26011604 | C2 | semidirect |
| 10. #26011593 | C2 | semidirect |
| 11. #432×C173 | C2 | semidirect |
| 17. #19149671 | C22 | semidirect |
| 18. #19149667 | C22 | semidirect |
| 22. C4×Dic346 | C22 | semidirect |
| 27. C4×D692 | C22 | semidirect |
| 32. #19149613 | C22 | semidirect |
| 33. #19149611 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 39. C4⋊C8×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 140. C173 | #3114 | semidirect |
| 152. #432 | D173 | semidirect |
| 176. C4⋊C8 | C2×D173 | semidirect |
| 183. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| C2×C4×D692 | 2 |
| #26011822 | 2 |
| #26011805 | 2 |
| #26011792 | 2 |
| #26011707 | 2 |
| #26011644 | 2 |
| #26011627 | 2 |
| #26011604 | 2 |
| #26011593 | 2 |
| #432×C173 | 2 |
| #3114 | 173 |