Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #26011585 | C2 | semidirect |
| 4. #26011316 | C2 | semidirect |
| 5. #26011296 | C2 | semidirect |
| 6. #26011266 | C2 | semidirect |
| 11. #19149623 | C4 | semidirect |
| 23. Dic692 | C2×C4 | semidirect |
| 30. #14583801 | C2×C4 | semidirect |
| 67. C173 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149623 | 2 |
| #26011585 | 2 |
| D8×Dic173 | 2 |
| #26011316 | 2 |
| #26011296 | 2 |
| #26011266 | 2 |
| #357×C173 | 2 |
| #2175 | 173 |