Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 81. C173 | #1636 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011843 | 2 |
| #26011786 | 2 |
| #26011237 | 2 |
| Q8⋊#13063436 | 2 |
| #557×C173 | 2 |
| #1636 | 173 |