Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C2×#19149611 | C2 | semidirect |
| 3. #26011302 | C2 | direct (N × H) |
| 4. C2×M32×C173 | C2 | semidirect |
| 8. #19149701 | C4 | semidirect |
| 10. C2×Dic692 | C4 | semidirect |
| 12. C2×D1384 | C4 | semidirect |
| 15. #19149611 | C22 | semidirect |
| 18. M32×C173 | C22 | semidirect |
| 30. Dic692 | C2×C4 | semidirect |
| 34. D1384 | C2×C4 | semidirect |
| 82. C2×C173 | #360 | semidirect |
| 85. C173 | C2×#360 | semidirect |
| 88. C2×M32 | D173 | semidirect |
| 102. M32 | C2×D173 | semidirect |
| 169. C2 | #26011302 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149611 | 2 |
| #26011302 | 2 |
| C2×M32×C173 | 2 |
| C2×#360 | 173 |