Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
756 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 198 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. #26012569 | C2 | semidirect |
| 2. #26012478 | C2 | semidirect |
| 3. #26012477 | C2 | semidirect |
| 4. D173⋊#100 | C2 | semidirect |
| 5. C2×#19149739 | C2 | semidirect |
| 8. D173⋊M16 | C22 | semidirect |
| 9. C2×#14583835 | C22 | semidirect |
| 10. #19149740 | C22 | semidirect |
| 11. #19149739 | C22 | semidirect |
| 12. #19149739 | C22 | semidirect |
| 131. C173 | #2888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012569 | 2 |
| #26012478 | 2 |
| #26012477 | 2 |
| D173⋊#100 | 2 |
| C2×#19149739 | 2 |
| C2×#19149724 | 2 |
| #2888 | 173 |