Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 12. #19149589 | C4 | semidirect |
| 13. C8×Dic173 | C4 | semidirect |
| 72. C173 | #1841 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×Dic173 | 2 |
| #26011262 | 2 |
| #26011252 | 2 |
| #26011250 | 2 |
| #26011249 | 2 |
| #26011247 | 2 |
| #344×C173 | 2 |
| #1841 | 173 |