Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 5. #19149746 | C4 | semidirect |
| 58. C173 | #1296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149746 | 2 |
| #26011360 | 2 |
| #1296 | 173 |