Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 9. #19149749 | C4 | semidirect |
| 12. C8×#10621924 | C4 | semidirect |
| 15. #19149612 | C4 | semidirect |
| 16. #19149611 | C4 | semidirect |
| 17. #106×C173 | C4 | semidirect |
| 68. C173 | #1772 | semidirect |
| 83. #106 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149749 | 2 |
| #26012456 | 2 |
| C2×C8×#10621924 | 2 |
| #26012361 | 2 |
| #26011526 | 2 |
| #1772 | 173 |