Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 202 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. #26012550 | C2 | direct (N × H) |
| 2. C2×#19149754 | C2 | semidirect |
| 3. C2×#19149753 | C2 | semidirect |
| 4. C2×D173⋊C16 | C2 | semidirect |
| 5. C22×#14583829 | C2 | semidirect |
| 7. #19149754 | C22 | semidirect |
| 8. #19149753 | C22 | semidirect |
| 9. D173⋊C16 | C22 | semidirect |
| 13. C2×#14583829 | C22 | semidirect |
| 66. C2×C173 | #504 | semidirect |
| 69. C173 | C2×#504 | semidirect |
| 137. C2 | #26012550 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012550 | 2 |
| C2×#19149754 | 2 |
| C2×#19149753 | 2 |
| C2×D173⋊C16 | 2 |
| C22×#14583829 | 2 |
| C2×#19149687 | 2 |
| C2×#504 | 173 |