Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 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. C2×#19149668 | C2 | semidirect |
| 4. #26011667 | C2 | direct (N × H) |
| 5. C2×#19149606 | C2 | semidirect |
| 6. C2×#19149605 | C2 | semidirect |
| 7. C2×#19149595 | C2 | semidirect |
| 8. C2×#137×C173 | C2 | semidirect |
| 21. #19149710 | C22 | semidirect |
| 24. C2×#14583810 | C22 | semidirect |
| 26. #19149668 | C22 | semidirect |
| 28. C2×C4×Dic173 | C22 | semidirect |
| 29. #19149606 | C22 | semidirect |
| 30. #19149605 | C22 | semidirect |
| 31. #19149595 | C22 | semidirect |
| 33. C22×Q8×C173 | C22 | semidirect |
| 35. #137×C173 | C22 | semidirect |
| 38. C2×M16×C173 | C22 | semidirect |
| 72. #14583810 | C23 | semidirect |
| 76. C4×Dic173 | C23 | semidirect |
| 87. C2×Q8×C173 | C23 | semidirect |
| 96. M16×C173 | C23 | semidirect |
| 173. C2×C173 | #455 | semidirect |
| 177. C173 | C2×#455 | semidirect |
| 181. C2×#137 | D173 | semidirect |
| 195. C22×Q8 | C2×D173 | semidirect |
| 203. #137 | C2×D173 | semidirect |
| 209. C2×M16 | C2×D173 | semidirect |
| 238. C2×Q8 | C22×D173 | semidirect |
| 270. M16 | C22×D173 | semidirect |
| 353. C2 | #26011667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149725 | 2 |
| C2×#19149710 | 2 |
| C2×#19149668 | 2 |
| #26011667 | 2 |
| C2×#19149606 | 2 |
| C2×#19149605 | 2 |
| C2×#19149595 | 2 |
| C2×#137×C173 | 2 |
| C2×#455 | 173 |