Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26011974 | C2 | semidirect |
| 3. #26011816 | C2 | semidirect |
| 4. #26011816 | C2 | semidirect |
| 5. #26011810 | C2 | semidirect |
| 6. #26011805 | C2 | semidirect |
| 7. #26011533 | C2 | semidirect |
| 8. #26011529 | C2 | semidirect |
| 9. #26011497 | C2 | semidirect |
| 10. C2×#19149601 | C2 | semidirect |
| 11. #408×C173 | C2 | semidirect |
| 23. #19149638 | C22 | semidirect |
| 25. C2×C4⋊Dic173 | C22 | semidirect |
| 26. #19149613 | C22 | semidirect |
| 27. #19149613 | C22 | semidirect |
| 28. #19149613 | C22 | semidirect |
| 29. #19149611 | C22 | semidirect |
| 30. #19149611 | C22 | semidirect |
| 31. #19149611 | C22 | semidirect |
| 39. C22⋊C8×C173 | C22 | semidirect |
| 40. C22⋊C8×C173 | C22 | semidirect |
| 134. C173 | #3096 | semidirect |
| 146. #408 | D173 | semidirect |
| 174. C22⋊C8 | C2×D173 | semidirect |
| 175. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012055 | 2 |
| #26011974 | 2 |
| #26011816 | 2 |
| #26011810 | 2 |
| #26011805 | 2 |
| #26011533 | 2 |
| #26011529 | 2 |
| #26011497 | 2 |
| C2×#19149601 | 2 |
| #408×C173 | 2 |
| #3096 | 173 |