Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic173 | C2 | semidirect |
| 3. C2×#19149605 | C2 | semidirect |
| 4. #26011464 | C2 | semidirect |
| 5. #26011262 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 7. #421×C173 | C2 | semidirect |
| 10. #19149709 | C4 | semidirect |
| 12. #19149704 | C4 | semidirect |
| 33. C2×Dic346 | C2×C4 | semidirect |
| 34. C2×D692 | C2×C4 | semidirect |
| 44. #14583810 | C2×C4 | semidirect |
| 129. C173 | #1906 | semidirect |
| 133. #421 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #41×Dic173 | 2 |
| C2×#19149605 | 2 |
| #26011464 | 2 |
| #26011262 | 2 |
| #26011250 | 2 |
| #421×C173 | 2 |
| #1906 | 173 |