Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1024 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1024 conjugacy classes of subgroups — too many to draw. Only its 469 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. #26012241 | C2 | direct (N × H) |
| 2. C2×#19149677 | C2 | semidirect |
| 3. C2×#19149672 | C2 | semidirect |
| 4. C2×#19149671 | C2 | semidirect |
| 6. C2×#19149656 | C2 | semidirect |
| 10. #19149677 | C22 | semidirect |
| 11. #19149672 | C22 | semidirect |
| 12. #19149671 | C22 | semidirect |
| 14. #19149656 | C22 | semidirect |
| 82. C2×C173 | #563 | semidirect |
| 85. C173 | C2×#563 | semidirect |
| 168. C2 | #26012241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012241 | 2 |
| C2×#19149677 | 2 |
| C2×#19149672 | 2 |
| C2×#19149671 | 2 |
| C2×#19149660 | 2 |
| C2×#19149656 | 2 |
| C2×#124×C173 | 2 |
| C2×#563 | 173 |