Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26011514 | C2 | semidirect |
| 4. C4×#14583805 | C2 | semidirect |
| 5. #26011252 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 9. Q8×Dic173 | C4 | semidirect |
| 10. Q8×Dic173 | C4 | semidirect |
| 13. D4×Dic173 | C4 | semidirect |
| 14. D4×Dic173 | C4 | semidirect |
| 86. Q8×C173 | C4⋊C4 | semidirect |
| 90. D4×C173 | C4⋊C4 | semidirect |
| 124. Dic173 | #104 | semidirect |
| 131. C173 | #1806 | semidirect |
| 204. Q8 | #14583805 | semidirect |
| 208. D4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×Dic173 | 2 |
| #26011514 | 2 |
| C2×#19149606 | 2 |
| C4×#14583805 | 2 |
| #26011252 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1806 | 173 |