Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 178 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 |
|---|---|---|
| 8. #19149733 | C4 | direct (N × H) |
| 9. C4×#13063443 | C4 | semidirect |
| 12. C4×#13063436 | C4 | semidirect |
| 13. C8×Dic173 | C4 | semidirect |
| 14. C4×C8×C173 | C4 | semidirect |
| 30. #13063443 | C42 | semidirect |
| 36. #13063436 | C42 | semidirect |
| 39. C8×C173 | C42 | semidirect |
| 44. C4×C173 | #97 | semidirect |
| 46. Dic173 | #97 | semidirect |
| 51. C173 | C4×#97 | semidirect |
| 66. C4×C8 | #10621924 | semidirect |
| 91. C8 | C4×#10621924 | semidirect |
| 98. C4 | #19149733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149733 | 2 |
| C4×D173⋊C8 | 2 |
| C42×#10621924 | 2 |
| C4×C8×D173 | 2 |
| C4×#97 | 173 |