Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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×#19149677 | C2 | semidirect |
| 3. #26011884 | C2 | semidirect |
| 4. #26011858 | C2 | semidirect |
| 5. #26011699 | C2 | semidirect |
| 6. #26011695 | C2 | semidirect |
| 7. #26011646 | C2 | semidirect |
| 10. #26011545 | C2 | semidirect |
| 11. #451×C173 | C2 | semidirect |
| 137. C173 | #3218 | semidirect |
| 146. #451 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149677 | 2 |
| #26012027 | 2 |
| #26011884 | 2 |
| #26011858 | 2 |
| #26011699 | 2 |
| #26011695 | 2 |
| #26011646 | 2 |
| #26011632 | 2 |
| #26011630 | 2 |
| #26011545 | 2 |
| #451×C173 | 2 |
| #3218 | 173 |