Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
428 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 10. #19149671 | C4 | semidirect |
| 98. C173 | #2336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149671 | 2 |
| #26011386 | 2 |
| #26011376 | 2 |
| #26011375 | 2 |
| #26011374 | 2 |
| #26011372 | 2 |
| #26011359 | 2 |
| C4×#14583805 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #2336 | 173 |