Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 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. C2×#19149710 | C2 | semidirect |
| 3. #26011673 | C2 | semidirect |
| 4. #26011668 | C2 | semidirect |
| 5. #26011509 | C2 | semidirect |
| 6. #26011475 | C2 | semidirect |
| 7. #536×C173 | C2 | semidirect |
| 17. #19149710 | C22 | semidirect |
| 20. C2×#14583810 | C22 | semidirect |
| 21. #19149607 | C22 | semidirect |
| 22. #19149598 | C22 | semidirect |
| 23. #19149596 | C22 | semidirect |
| 25. C22×Q8×C173 | C22 | semidirect |
| 26. C4⋊Q8×C173 | C22 | semidirect |
| 27. #124×C173 | C22 | semidirect |
| 30. #117×C173 | C22 | semidirect |
| 129. C173 | #3022 | semidirect |
| 133. #536 | D173 | semidirect |
| 147. C22×Q8 | C2×D173 | semidirect |
| 153. C4⋊Q8 | C2×D173 | semidirect |
| 154. #124 | C2×D173 | semidirect |
| 157. #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 |
| C2×#19149710 | 2 |
| #26011673 | 2 |
| #26011668 | 2 |
| #26011509 | 2 |
| #26011475 | 2 |
| #536×C173 | 2 |
| #3022 | 173 |