Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012042 | C2 | semidirect |
| 2. C4×#14583825 | C2 | semidirect |
| 3. #26011818 | C2 | semidirect |
| 4. #26011773 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011686 | C2 | semidirect |
| 7. #26011637 | C2 | semidirect |
| 8. #26011600 | C2 | semidirect |
| 9. #26011590 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #474×C173 | C2 | semidirect |
| 86. Dic346 | #41 | semidirect |
| 109. D4×C173 | #41 | semidirect |
| 144. C173 | #3115 | semidirect |
| 150. #474 | D173 | semidirect |
| 241. D4 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| C4×#14583825 | 2 |
| #26011818 | 2 |
| #26011773 | 2 |
| #26011692 | 2 |
| #26011686 | 2 |
| #26011637 | 2 |
| #26011600 | 2 |
| #26011590 | 2 |
| #26011547 | 2 |
| #474×C173 | 2 |
| #3115 | 173 |