Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 4. #26011258 | C2 | semidirect |
| 5. #26011257 | C2 | semidirect |
| 6. #26011257 | C2 | semidirect |
| 7. #342×C173 | C2 | semidirect |
| 11. #19149635 | C4 | semidirect |
| 15. C22⋊C4×D173 | C4 | semidirect |
| 118. C173 | #1828 | semidirect |
| 126. #342 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011964 | 2 |
| C2×#19149593 | 2 |
| #26011258 | 2 |
| #26011257 | 2 |
| #342×C173 | 2 |
| #1828 | 173 |