Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
160 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 65 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. Q16×Dic173 | C2 | semidirect |
| 3. #26011317 | C2 | semidirect |
| 4. #26011295 | C2 | semidirect |
| 6. #26011266 | C2 | semidirect |
| 18. SD32×C173 | C4 | semidirect |
| 32. Q16×C173 | C2×C4 | semidirect |
| 36. C16×C173 | C2×C4 | semidirect |
| 67. C173 | #2175 | semidirect |
| 80. SD32 | Dic173 | semidirect |
| 92. Q16 | C2×Dic173 | semidirect |
| 104. C16 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic173 | 2 |
| D8×Dic173 | 2 |
| #26011317 | 2 |
| #26011295 | 2 |
| #26011292 | 2 |
| #26011266 | 2 |
| C2×SD32×C173 | 2 |
| #2175 | 173 |