Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26011608 | C2 | semidirect |
| 3. #26011607 | C2 | semidirect |
| 4. #26011320 | C2 | semidirect |
| 5. #26011299 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. #359×C173 | C2 | semidirect |
| 11. #19149625 | C4 | semidirect |
| 12. #19149623 | C4 | semidirect |
| 13. #19149622 | C4 | semidirect |
| 14. #19149620 | C4 | semidirect |
| 71. C173 | #2178 | semidirect |
| 78. #359 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011921 | 2 |
| #26011608 | 2 |
| #26011607 | 2 |
| #26011320 | 2 |
| #26011299 | 2 |
| C16×Dic173 | 2 |
| #359×C173 | 2 |
| #2178 | 173 |