Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19149699 | C2 | semidirect |
| 2. #26012041 | C2 | semidirect |
| 3. #26011886 | C2 | semidirect |
| 4. #26011883 | C2 | semidirect |
| 5. #26011881 | C2 | semidirect |
| 6. #26011878 | C2 | semidirect |
| 7. C2×#19149590 | C2 | semidirect |
| 8. #532×C173 | C2 | semidirect |
| 40. C2×#13063436 | D4 | semidirect |
| 97. C173 | #3150 | semidirect |
| 101. #532 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| #26012041 | 2 |
| #26011886 | 2 |
| #26011883 | 2 |
| #26011881 | 2 |
| #26011878 | 2 |
| C2×#19149590 | 2 |
| #532×C173 | 2 |
| #3150 | 173 |