Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26011545 | C2 | semidirect |
| 3. #26011336 | C2 | semidirect |
| 4. #26011226 | C2 | semidirect |
| 5. #26011225 | C2 | semidirect |
| 6. #26011224 | C2 | semidirect |
| 7. #327×C173 | C2 | semidirect |
| 9. #19149678 | C4 | semidirect |
| 10. #19149675 | C4 | semidirect |
| 14. D4×Dic173 | C4 | semidirect |
| 15. #19149641 | C4 | semidirect |
| 119. C173 | #1505 | semidirect |
| 127. #327 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| #26011545 | 2 |
| #26011336 | 2 |
| #26011226 | 2 |
| #26011225 | 2 |
| #26011224 | 2 |
| #327×C173 | 2 |
| #1505 | 173 |