Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 7. #19149596 | C4 | semidirect |
| 9. #19149594 | C4 | semidirect |
| 11. C23×C4×C173 | C4 | semidirect |
| 13. C2×C22⋊C4×C173 | C4 | semidirect |
| 102. C173 | #1390 | semidirect |
| 108. C23×C4 | Dic173 | semidirect |
| 112. C2×C22⋊C4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149596 | 2 |
| C2×#19149594 | 2 |
| #386×C173 | 2 |
| #1390 | 173 |