Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011852 | C2 | semidirect |
| 5. #26011851 | C2 | semidirect |
| 6. #26011850 | C2 | semidirect |
| 7. #26011849 | C2 | semidirect |
| 8. #103×D173 | C2 | semidirect |
| 10. #97×D173 | C2 | semidirect |
| 11. #489×C173 | C2 | semidirect |
| 16. #19149679 | C22 | semidirect |
| 18. #19149678 | C22 | semidirect |
| 30. #19149604 | C22 | semidirect |
| 31. #19149603 | C22 | semidirect |
| 32. #19149602 | C22 | semidirect |
| 36. #19149590 | C22 | semidirect |
| 37. #19149589 | C22 | semidirect |
| 38. C4⋊Q8×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 140. D173 | #489 | direct (N × H) |
| 141. C173 | C2×#489 | semidirect |
| 150. #489 | D173 | direct (N × H) |
| 162. C4⋊Q8 | C2×D173 | semidirect |
| 177. #103 | C2×D173 | semidirect |
| 184. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #124×D173 | 2 |
| #26011853 | 2 |
| #26011852 | 2 |
| #26011851 | 2 |
| #26011850 | 2 |
| #26011849 | 2 |
| #103×D173 | 2 |
| #102×D173 | 2 |
| #97×D173 | 2 |
| #489×C173 | 2 |
| C2×#489 | 173 |