Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 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 |
|---|---|---|
| 3. #26011599 | C2 | semidirect |
| 4. #26011314 | C2 | semidirect |
| 5. #26011308 | C2 | semidirect |
| 7. #347×C173 | C2 | semidirect |
| 12. Dic1384 | C4 | semidirect |
| 13. #19149624 | C4 | semidirect |
| 64. C173 | #2180 | semidirect |
| 72. #347 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011934 | 2 |
| #26011614 | 2 |
| #26011599 | 2 |
| #26011314 | 2 |
| #26011308 | 2 |
| #26011302 | 2 |
| #347×C173 | 2 |
| #2180 | 173 |