Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #26011447 | C2 | semidirect |
| 4. C2×#19149589 | C2 | semidirect |
| 5. #26011256 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 9. #19149686 | C4 | semidirect |
| 16. #19149606 | C4 | semidirect |
| 23. #103×C173 | C4 | semidirect |
| 24. #102×C173 | C4 | semidirect |
| 98. C173 | #1765 | semidirect |
| 119. #103 | Dic173 | semidirect |
| 120. #102 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| C2×#19149606 | 2 |
| #26011447 | 2 |
| C2×#19149589 | 2 |
| #26011256 | 2 |
| #26011250 | 2 |
| #416×C173 | 2 |
| #1765 | 173 |