Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 4. C2×C4⋊#10621924 | C4 | semidirect |
| 8. C2×C4×#10621924 | C4 | semidirect |
| 9. #19149738 | C4 | semidirect |
| 13. #19149594 | C4 | semidirect |
| 15. #99×C173 | C4 | semidirect |
| 107. C173 | #1393 | semidirect |
| 123. #99 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#99 | 2 |
| #26012443 | 2 |
| #99×D173 | 2 |
| #1393 | 173 |