Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. #26012065 | C2 | semidirect |
| 4. #26011650 | C2 | semidirect |
| 5. #26011640 | C2 | semidirect |
| 6. #26011496 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. #26011457 | C2 | semidirect |
| 9. C22×SD16×C173 | C2 | semidirect |
| 20. C2×#14583816 | C22 | semidirect |
| 21. C2×#14583813 | C22 | semidirect |
| 22. C2×#14583810 | C22 | semidirect |
| 26. #19149655 | C22 | semidirect |
| 27. #19149638 | C22 | semidirect |
| 28. #19149604 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 30. #19149600 | C22 | semidirect |
| 31. #19149591 | C22 | semidirect |
| 32. C22×Q8×C173 | C22 | semidirect |
| 35. C2×SD16×C173 | C22 | semidirect |
| 36. C22×C8×C173 | C22 | semidirect |
| 146. C173 | #3009 | semidirect |
| 150. C22×SD16 | D173 | semidirect |
| 163. C22×Q8 | C2×D173 | semidirect |
| 172. C2×SD16 | C2×D173 | semidirect |
| 174. C22×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149710 | 2 |
| #26012065 | 2 |
| #26011650 | 2 |
| #26011640 | 2 |
| #26011496 | 2 |
| #26011488 | 2 |
| #26011457 | 2 |
| C22×SD16×C173 | 2 |
| #3009 | 173 |