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×#19149704 | C2 | semidirect |
| 2. C2×C4×D692 | C2 | semidirect |
| 3. #26011703 | C2 | semidirect |
| 4. #26011693 | C2 | semidirect |
| 5. #26011683 | C2 | semidirect |
| 6. #26011515 | C2 | semidirect |
| 7. #26011492 | C2 | semidirect |
| 8. #532×C173 | C2 | semidirect |
| 21. C4⋊#13063436 | C22 | semidirect |
| 22. C4⋊#13063436 | C22 | semidirect |
| 23. #19149603 | C22 | semidirect |
| 24. #19149600 | C22 | semidirect |
| 26. C4⋊Q8×C173 | C22 | semidirect |
| 27. #127×C173 | C22 | semidirect |
| 28. #124×C173 | C22 | semidirect |
| 37. C2×D692 | D4 | semidirect |
| 119. C4×C173 | AGL(1,ℤ/8) | semidirect |
| 129. C173 | #3036 | semidirect |
| 132. #532 | D173 | semidirect |
| 146. C4⋊Q8 | C2×D173 | semidirect |
| 147. #127 | C2×D173 | semidirect |
| 148. #124 | C2×D173 | semidirect |
| 250. C4 | #19149704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C2×C4×D692 | 2 |
| #26011703 | 2 |
| #26011693 | 2 |
| #26011683 | 2 |
| #26011515 | 2 |
| #26011492 | 2 |
| #532×C173 | 2 |
| #3036 | 173 |