Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19149658 | C2 | semidirect |
| 3. #26011822 | C2 | semidirect |
| 4. #26011810 | C2 | semidirect |
| 5. #26011720 | C2 | semidirect |
| 6. #26011644 | C2 | semidirect |
| 7. #26011632 | C2 | semidirect |
| 8. C2×C22⋊C8×C173 | C2 | semidirect |
| 9. C22×Dic346 | C22 | semidirect |
| 12. C2×#14583815 | C22 | semidirect |
| 16. #19149658 | C22 | semidirect |
| 22. C2×C4⋊Dic173 | C22 | semidirect |
| 26. #19149611 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 30. C22×C8×C173 | C22 | semidirect |
| 32. C22⋊C8×C173 | C22 | semidirect |
| 85. C23×C173 | SD16 | semidirect |
| 129. C173 | #3187 | semidirect |
| 138. C2×C22⋊C8 | D173 | semidirect |
| 144. C22×C8 | C2×D173 | semidirect |
| 162. C22⋊C8 | C2×D173 | semidirect |
| 203. C23 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149658 | 2 |
| C2×#19149653 | 2 |
| #26011822 | 2 |
| #26011810 | 2 |
| #26011720 | 2 |
| #26011644 | 2 |
| #26011632 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #3187 | 173 |