Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 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 |
|---|---|---|
| 1. C2×#19149724 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C2×#19149675 | C2 | semidirect |
| 4. #26011661 | C2 | direct (N × H) |
| 5. C2×#19149605 | C2 | semidirect |
| 6. C2×#100×C173 | C2 | semidirect |
| 9. #19149724 | C22 | semidirect |
| 12. C22×D692 | C22 | semidirect |
| 17. #19149707 | C22 | semidirect |
| 21. #19149675 | C22 | semidirect |
| 22. C2×C4×Dic173 | C22 | semidirect |
| 23. #19149605 | C22 | semidirect |
| 25. C2×M16×C173 | C22 | semidirect |
| 26. #100×C173 | C22 | semidirect |
| 31. #14583826 | D4 | semidirect |
| 35. C2×Dic346 | D4 | semidirect |
| 39. C2×D692 | D4 | semidirect |
| 40. C2×D692 | C23 | semidirect |
| 55. C4×Dic173 | C23 | semidirect |
| 63. M16×C173 | C23 | semidirect |
| 73. Dic346 | C2×D4 | semidirect |
| 77. D692 | C2×D4 | semidirect |
| 122. C2×C173 | #453 | semidirect |
| 126. C173 | C2×#453 | semidirect |
| 133. C2×#100 | D173 | semidirect |
| 148. C2×M16 | C2×D173 | semidirect |
| 153. #100 | C2×D173 | semidirect |
| 188. M16 | C22×D173 | semidirect |
| 251. C2 | #26011661 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149707 | 2 |
| C2×#19149675 | 2 |
| #26011661 | 2 |
| C2×#19149605 | 2 |
| C2×#100×C173 | 2 |
| C2×#453 | 173 |