Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
212 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #26011233 | C2 | semidirect |
| 72. C173 | #1531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011548 | 2 |
| C2×#19149590 | 2 |
| #26011233 | 2 |
| #533×C173 | 2 |
| #1531 | 173 |