Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C2×#19149677 | C2 | semidirect |
| 3. #26011862 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 5. #26011695 | C2 | semidirect |
| 6. #26011694 | C2 | semidirect |
| 7. #26011632 | C2 | semidirect |
| 8. #26011630 | C2 | semidirect |
| 9. #26011629 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #448×C173 | C2 | semidirect |
| 99. C2×Dic173 | SD16 | semidirect |
| 146. C173 | #3206 | semidirect |
| 157. #448 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| C2×#19149677 | 2 |
| #26011862 | 2 |
| #26011840 | 2 |
| #26011695 | 2 |
| #26011694 | 2 |
| #26011632 | 2 |
| #26011630 | 2 |
| #26011629 | 2 |
| #26011541 | 2 |
| #448×C173 | 2 |
| #3206 | 173 |