Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26011531 | C2 | semidirect |
| 5. #26011449 | C2 | semidirect |
| 6. #26011255 | C2 | semidirect |
| 7. #343×C173 | C2 | semidirect |
| 18. #19149595 | C4 | semidirect |
| 100. C173 | #1931 | semidirect |
| 107. #343 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011531 | 2 |
| #26011497 | 2 |
| C2×#19149599 | 2 |
| C2×#19149595 | 2 |
| #26011449 | 2 |
| #26011255 | 2 |
| #343×C173 | 2 |
| #1931 | 173 |