Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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×#19149726 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C2×#19149704 | C2 | semidirect |
| 4. C2×#19149667 | C2 | semidirect |
| 5. #26011665 | C2 | direct (N × H) |
| 6. C2×#19149607 | C2 | semidirect |
| 7. C2×#19149597 | C2 | semidirect |
| 8. C2×#104×C173 | C2 | semidirect |
| 12. #19149726 | C22 | semidirect |
| 22. #19149707 | C22 | semidirect |
| 24. #19149704 | C22 | semidirect |
| 31. #19149667 | C22 | semidirect |
| 33. #19149607 | C22 | semidirect |
| 34. #19149597 | C22 | semidirect |
| 38. #104×C173 | C22 | semidirect |
| 171. C2×C173 | #454 | semidirect |
| 175. C173 | C2×#454 | semidirect |
| 183. C2×#104 | D173 | semidirect |
| 213. #104 | C2×D173 | semidirect |
| 349. C2 | #26011665 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149726 | 2 |
| C2×#19149707 | 2 |
| C2×#19149704 | 2 |
| C2×#19149667 | 2 |
| #26011665 | 2 |
| C2×#19149607 | 2 |
| C2×#19149597 | 2 |
| C2×#104×C173 | 2 |
| C2×#454 | 173 |