Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 3. #26011281 | C2 | semidirect |
| 12. C22×Q8×C173 | C4 | semidirect |
| 15. #123×C173 | C4 | semidirect |
| 19. #117×C173 | C4 | semidirect |
| 92. C173 | #2123 | semidirect |
| 99. C22×Q8 | Dic173 | semidirect |
| 103. #123 | Dic173 | semidirect |
| 108. #117 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011475 | 2 |
| #26011465 | 2 |
| #26011281 | 2 |
| #536×C173 | 2 |
| #2123 | 173 |