Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19149711 | C2 | semidirect |
| 2. #26012156 | C2 | semidirect |
| 4. #26011746 | C2 | semidirect |
| 5. #26011698 | C2 | semidirect |
| 6. #26011693 | C2 | semidirect |
| 7. #26011652 | C2 | semidirect |
| 8. #26011645 | C2 | semidirect |
| 9. C4×#14583815 | C2 | semidirect |
| 10. #26011570 | C2 | semidirect |
| 11. #494×C173 | C2 | semidirect |
| 56. #14583815 | D4 | semidirect |
| 122. C4×C173 | #137 | semidirect |
| 134. C173 | #3276 | semidirect |
| 139. #494 | D173 | semidirect |
| 261. C4 | #19149711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149711 | 2 |
| #26012156 | 2 |
| #26012144 | 2 |
| #26011746 | 2 |
| #26011698 | 2 |
| #26011693 | 2 |
| #26011652 | 2 |
| #26011645 | 2 |
| C4×#14583815 | 2 |
| #26011570 | 2 |
| #494×C173 | 2 |
| #3276 | 173 |