Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. C4⋊Q8×D173 | C2 | semidirect |
| 4. #26011702 | C2 | semidirect |
| 5. #26011700 | C2 | semidirect |
| 6. #26011698 | C2 | semidirect |
| 7. #26011696 | C2 | semidirect |
| 8. #26011694 | C2 | semidirect |
| 9. #26011513 | C2 | semidirect |
| 10. #26011498 | C2 | semidirect |
| 11. #461×C173 | C2 | semidirect |
| 131. C4×C173 | #137 | semidirect |
| 139. Dic173 | #137 | semidirect |
| 145. C173 | #3039 | semidirect |
| 155. #461 | D173 | semidirect |
| 283. C4 | #19149708 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149708 | 2 |
| C4⋊Q8×D173 | 2 |
| C4×#14583825 | 2 |
| #26011702 | 2 |
| #26011700 | 2 |
| #26011698 | 2 |
| #26011696 | 2 |
| #26011694 | 2 |
| #26011513 | 2 |
| #26011498 | 2 |
| #461×C173 | 2 |
| #3039 | 173 |