Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
592 conjugacy classes of subgroups; only the 298 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 298 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 |
|---|---|---|
| 3. #26012456 | C2 | direct (N × H) |
| 4. C2×#19149734 | C2 | semidirect |
| 5. C2×C4×#13063443 | C2 | semidirect |
| 7. C2×#14583836 | C4 | semidirect |
| 9. C2×D173⋊C8 | C4 | semidirect |
| 14. #19149734 | C22 | semidirect |
| 15. C4×#13063443 | C22 | semidirect |
| 23. #14583836 | C2×C4 | semidirect |
| 24. D173⋊C8 | C2×C4 | semidirect |
| 80. C2×C173 | #405 | semidirect |
| 85. C173 | C2×#405 | semidirect |
| 167. C2 | #26012456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C22×D173⋊C8 | 2 |
| #26012456 | 2 |
| C2×#19149734 | 2 |
| C2×C4×#13063443 | 2 |
| C2×#19149637 | 2 |
| C2×#405 | 173 |