Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×Q8×Dic173 | C2 | semidirect |
| 5. #26011380 | C2 | semidirect |
| 6. #26011365 | C2 | semidirect |
| 7. #26011360 | C2 | semidirect |
| 8. #26011337 | C2 | semidirect |
| 9. #391×C173 | C2 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 45. #14583803 | C2×C4 | semidirect |
| 47. C4×Dic173 | C2×C4 | semidirect |
| 51. C2×Q8×C173 | C2×C4 | semidirect |
| 111. C173 | #2326 | semidirect |
| 116. #391 | D173 | semidirect |
| 145. C2×Q8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149668 | 2 |
| C2×Q8×Dic173 | 2 |
| C2×#19149641 | 2 |
| #26011393 | 2 |
| #26011380 | 2 |
| #26011365 | 2 |
| #26011360 | 2 |
| #26011337 | 2 |
| #391×C173 | 2 |
| #2326 | 173 |