Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26011268 | C2 | semidirect |
| 7. #19149619 | C4 | semidirect |
| 9. C2×#14583801 | C4 | semidirect |
| 13. M32×C173 | C4 | semidirect |
| 15. C2×C16×C173 | C4 | semidirect |
| 57. C173 | #2110 | semidirect |
| 68. M32 | Dic173 | semidirect |
| 71. C2×C16 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149619 | 2 |
| #26011446 | 2 |
| #26011268 | 2 |
| C2×M32×C173 | 2 |
| #2110 | 173 |