Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#19149677 | C2 | semidirect |
| 4. #26011699 | C2 | semidirect |
| 5. #26011694 | C2 | semidirect |
| 6. #26011514 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011500 | C2 | semidirect |
| 116. Dic173 | #137 | semidirect |
| 121. C173 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149677 | 2 |
| #41×Dic173 | 2 |
| #26011699 | 2 |
| #26011694 | 2 |
| #26011514 | 2 |
| #26011501 | 2 |
| #26011500 | 2 |
| C2×#137×C173 | 2 |
| #3039 | 173 |