Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012041 | C2 | semidirect |
| 2. C2×#19149667 | C2 | semidirect |
| 3. #26011880 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011707 | C2 | semidirect |
| 6. #26011632 | C2 | semidirect |
| 7. #26011627 | C2 | semidirect |
| 8. #432×C173 | C2 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 15. #19149676 | C22 | semidirect |
| 24. C4×D692 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 30. C4⋊C8×C173 | C22 | semidirect |
| 32. #97×C173 | C22 | semidirect |
| 120. C173 | #3213 | semidirect |
| 129. #432 | D173 | semidirect |
| 149. C4⋊C8 | C2×D173 | semidirect |
| 153. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149667 | 2 |
| #26011880 | 2 |
| #26011851 | 2 |
| #26011707 | 2 |
| #26011632 | 2 |
| #26011627 | 2 |
| #432×C173 | 2 |
| #3213 | 173 |