Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
696 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 325 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. C4×#14583805 | C2 | semidirect |
| 4. #26011342 | C2 | semidirect |
| 10. #19149635 | C4 | semidirect |
| 11. C2×#14583805 | C4 | semidirect |
| 34. #14583805 | C2×C4 | semidirect |
| 38. C4×Dic173 | C2×C4 | semidirect |
| 51. C2×Dic173 | C42 | semidirect |
| 89. C173 | #2274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149635 | 2 |
| C22×#14583805 | 2 |
| C4×#14583805 | 2 |
| #26011342 | 2 |
| C22⋊C4×Dic173 | 2 |
| C4×C22⋊Dic173 | 2 |
| C4×C22⋊C4×C173 | 2 |
| #2274 | 173 |