Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
568 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 197 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. #26011359 | C2 | semidirect |
| 3. #26011355 | C2 | semidirect |
| 6. #26011342 | C2 | semidirect |
| 8. #26011336 | C2 | semidirect |
| 9. #383×C173 | C2 | semidirect |
| 19. C42×D173 | C4 | semidirect |
| 97. C173 | #2283 | semidirect |
| 101. #383 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D173 | 2 |
| #26011359 | 2 |
| #26011355 | 2 |
| #26011353 | 2 |
| #26011350 | 2 |
| #26011342 | 2 |
| #26011338 | 2 |
| #26011336 | 2 |
| #383×C173 | 2 |
| #2283 | 173 |