Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26012065 | C2 | semidirect |
| 3. #26011680 | C2 | semidirect |
| 4. #26011465 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #536×C173 | C2 | semidirect |
| 17. #19149662 | C22 | semidirect |
| 19. #19149638 | C22 | semidirect |
| 20. #19149594 | C22 | semidirect |
| 21. #19149593 | C22 | semidirect |
| 23. C22×Q8×C173 | C22 | semidirect |
| 26. #123×C173 | C22 | semidirect |
| 28. #117×C173 | C22 | semidirect |
| 128. C173 | #3028 | semidirect |
| 132. #536 | D173 | semidirect |
| 145. C22×Q8 | C2×D173 | semidirect |
| 151. #123 | C2×D173 | semidirect |
| 155. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012327 | 2 |
| #26012065 | 2 |
| #26011680 | 2 |
| #26011465 | 2 |
| #26011464 | 2 |
| #536×C173 | 2 |
| #3028 | 173 |