Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
286 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26011534 | C2 | semidirect |
| 5. #26011357 | C2 | semidirect |
| 6. #26011259 | C2 | semidirect |
| 7. #339×C173 | C2 | semidirect |
| 19. #19149607 | C4 | semidirect |
| 38. #14583810 | C2×C4 | semidirect |
| 57. C42×C173 | C2×C4 | semidirect |
| 111. C173 | #1860 | semidirect |
| 119. #339 | D173 | semidirect |
| 169. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011971 | 2 |
| #26011534 | 2 |
| C2×#19149607 | 2 |
| #26011493 | 2 |
| #26011357 | 2 |
| #26011259 | 2 |
| #339×C173 | 2 |
| #1860 | 173 |