Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 23. #19149598 | C4 | semidirect |
| 24. #19149597 | C4 | semidirect |
| 25. #19149597 | C4 | semidirect |
| 26. #101×C173 | C4 | semidirect |
| 105. C173 | #1930 | semidirect |
| 130. #101 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012502 | 2 |
| #26012484 | 2 |
| C2×#19149742 | 2 |
| #26012457 | 2 |
| #26012370 | 2 |
| #26012366 | 2 |
| #101×D173 | 2 |
| #1930 | 173 |