Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 1. C2×#19149702 | C2 | semidirect |
| 2. C22×C8×D173 | C2 | semidirect |
| 3. #26012004 | C2 | semidirect |
| 4. #26011729 | C2 | semidirect |
| 5. #26011728 | C2 | semidirect |
| 6. #26011727 | C2 | semidirect |
| 7. #26011723 | C2 | semidirect |
| 8. #26011722 | C2 | semidirect |
| 9. #26011528 | C2 | semidirect |
| 10. #26011486 | C2 | semidirect |
| 11. #467×C173 | C2 | semidirect |
| 15. C2×#14583813 | C22 | semidirect |
| 16. C2×D1384 | C22 | semidirect |
| 31. #19149613 | C22 | semidirect |
| 32. #19149610 | C22 | semidirect |
| 33. #19149603 | C22 | semidirect |
| 34. #19149601 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 36. C2×Q16×C173 | C22 | semidirect |
| 39. #107×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 64. C8×D173 | D4 | semidirect |
| 118. C22×C173 | #135 | semidirect |
| 129. C2×D173 | #135 | semidirect |
| 145. C173 | #3050 | semidirect |
| 151. #467 | D173 | semidirect |
| 161. C2×Q16 | C2×D173 | semidirect |
| 181. #107 | C2×D173 | semidirect |
| 184. #103 | C2×D173 | semidirect |
| 274. C22 | #19149702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C22×C8×D173 | 2 |
| #26012004 | 2 |
| #26011729 | 2 |
| #26011728 | 2 |
| #26011727 | 2 |
| #26011723 | 2 |
| #26011722 | 2 |
| #26011528 | 2 |
| #26011486 | 2 |
| #467×C173 | 2 |
| #3050 | 173 |