Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
476 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 293 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. #26011533 | C2 | semidirect |
| 3. #26011529 | C2 | semidirect |
| 4. C2×#19149611 | C2 | semidirect |
| 15. #131×C173 | C4 | semidirect |
| 29. M16×C173 | C2×C4 | semidirect |
| 30. C2×C8×C173 | C2×C4 | semidirect |
| 56. C173 | #2912 | semidirect |
| 64. #131 | Dic173 | semidirect |
| 81. M16 | C2×Dic173 | semidirect |
| 82. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| #26011533 | 2 |
| #26011529 | 2 |
| C2×#19149611 | 2 |
| C2×#131×C173 | 2 |
| #2912 | 173 |