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 |
|---|---|---|
| 1. #26012258 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. #26011250 | C2 | semidirect |
| 5. #410×C173 | C2 | semidirect |
| 10. #19149677 | C4 | semidirect |
| 11. #19149675 | C4 | semidirect |
| 12. #19149668 | C4 | semidirect |
| 13. #19149666 | C4 | semidirect |
| 31. #14583810 | D4 | semidirect |
| 95. C173 | #1884 | semidirect |
| 100. #410 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012258 | 2 |
| #26012037 | 2 |
| #26011509 | 2 |
| #26011250 | 2 |
| #410×C173 | 2 |
| #1884 | 173 |