Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 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×#19149708 | C2 | semidirect |
| 2. C2×#19149703 | C2 | semidirect |
| 3. #26012039 | C2 | semidirect |
| 4. #124×D173 | C2 | semidirect |
| 5. #26011886 | C2 | semidirect |
| 6. #26011885 | C2 | semidirect |
| 7. #26011878 | C2 | semidirect |
| 8. #26011874 | C2 | semidirect |
| 9. #26011872 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 17. C2×Dic692 | C22 | semidirect |
| 18. C2×#14583816 | C22 | semidirect |
| 21. C2×#14583814 | C22 | semidirect |
| 24. #19149679 | C22 | semidirect |
| 28. #19149666 | C22 | semidirect |
| 34. #19149590 | C22 | semidirect |
| 35. C8×Dic173 | C22 | semidirect |
| 36. C2×SD16×C173 | C22 | semidirect |
| 38. #127×C173 | C22 | semidirect |
| 40. #97×C173 | C22 | semidirect |
| 62. #14583809 | D4 | semidirect |
| 134. C173 | #3153 | semidirect |
| 143. #496 | D173 | semidirect |
| 157. C2×SD16 | C2×D173 | semidirect |
| 162. #127 | C2×D173 | semidirect |
| 174. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149708 | 2 |
| C2×#19149703 | 2 |
| #26012039 | 2 |
| #124×D173 | 2 |
| #26011886 | 2 |
| #26011885 | 2 |
| #26011878 | 2 |
| #26011874 | 2 |
| #26011872 | 2 |
| #26011443 | 2 |
| #496×C173 | 2 |
| #3153 | 173 |