Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
220 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 9. #19149614 | C4 | semidirect |
| 50. C173 | #1778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149614 | 2 |
| M16×Dic173 | 2 |
| C2×#19149589 | 2 |
| #26011256 | 2 |
| #341×C173 | 2 |
| #1778 | 173 |