Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 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. C2×#19149707 | C2 | semidirect |
| 2. #26012041 | C2 | semidirect |
| 3. C2×C4×D692 | C2 | semidirect |
| 4. #26011707 | C2 | semidirect |
| 5. #26011697 | C2 | semidirect |
| 6. #26011687 | C2 | semidirect |
| 7. #26011493 | C2 | semidirect |
| 8. #423×C173 | C2 | semidirect |
| 15. #19149679 | C22 | semidirect |
| 16. #19149676 | C22 | semidirect |
| 17. #19149667 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 32. C4⋊C8×C173 | C22 | semidirect |
| 33. C4⋊C8×C173 | C22 | semidirect |
| 42. C2×D692 | D4 | semidirect |
| 118. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 129. C173 | #3036 | semidirect |
| 137. #423 | D173 | semidirect |
| 160. C4⋊C8 | C2×D173 | semidirect |
| 161. C4⋊C8 | C2×D173 | semidirect |
| 250. C4 | #19149707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26012041 | 2 |
| C2×C4×D692 | 2 |
| #26011707 | 2 |
| #26011697 | 2 |
| #26011687 | 2 |
| #26011493 | 2 |
| #423×C173 | 2 |
| #3036 | 173 |