Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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×#19149586 | C2 | semidirect |
| 3. #26011229 | C2 | semidirect |
| 4. #26011226 | C2 | semidirect |
| 5. #407×C173 | C2 | semidirect |
| 6. C2×#14583826 | C4 | semidirect |
| 9. #19149658 | C4 | semidirect |
| 11. #19149653 | C4 | semidirect |
| 16. #19149638 | C4 | semidirect |
| 24. C2×Dic346 | C2×C4 | semidirect |
| 25. C2×D692 | C2×C4 | semidirect |
| 34. C4⋊Dic173 | C2×C4 | semidirect |
| 35. C4⋊Dic173 | C2×C4 | semidirect |
| 119. C173 | #1504 | semidirect |
| 122. #407 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| C2×#19149586 | 2 |
| #26011229 | 2 |
| #26011226 | 2 |
| #407×C173 | 2 |
| #1504 | 173 |