Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #26011391 | C2 | semidirect |
| 3. #26011380 | C2 | semidirect |
| 4. #26011376 | C2 | semidirect |
| 5. #26011369 | C2 | semidirect |
| 6. #26011367 | C2 | semidirect |
| 7. C4×C22⋊Dic173 | C2 | semidirect |
| 8. #26011338 | C2 | semidirect |
| 9. #381×C173 | C2 | semidirect |
| 13. #19149653 | C4 | semidirect |
| 38. C2×C22⋊D173 | C2×C4 | semidirect |
| 45. C4⋊Dic173 | C2×C4 | semidirect |
| 51. #14583803 | C2×C4 | semidirect |
| 58. C22×C4×C173 | C2×C4 | semidirect |
| 134. C173 | #2333 | semidirect |
| 142. #381 | D173 | semidirect |
| 183. C22×C4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| #26011391 | 2 |
| #26011380 | 2 |
| #26011376 | 2 |
| #26011369 | 2 |
| #26011367 | 2 |
| C4×C22⋊Dic173 | 2 |
| #26011338 | 2 |
| #381×C173 | 2 |
| #2333 | 173 |