Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #26011518 | C2 | semidirect |
| 4. C2×#19149589 | C2 | semidirect |
| 5. #26011256 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 19. #103×C173 | C4 | semidirect |
| 20. #102×C173 | C4 | semidirect |
| 90. C173 | #1938 | semidirect |
| 108. #103 | Dic173 | semidirect |
| 109. #102 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011518 | 2 |
| C2×#19149606 | 2 |
| #26011458 | 2 |
| C2×#19149589 | 2 |
| #26011256 | 2 |
| #26011250 | 2 |
| #416×C173 | 2 |
| #1938 | 173 |