Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#19149638 | C2 | semidirect |
| 3. #26011816 | C2 | semidirect |
| 4. #26011810 | C2 | semidirect |
| 5. #26011805 | C2 | semidirect |
| 6. #26011533 | C2 | semidirect |
| 7. #26011497 | C2 | semidirect |
| 8. #407×C173 | C2 | semidirect |
| 18. #19149638 | C22 | semidirect |
| 20. C2×C4⋊Dic173 | C22 | semidirect |
| 21. C2×C4⋊Dic173 | C22 | semidirect |
| 25. #19149613 | C22 | semidirect |
| 26. #19149611 | C22 | semidirect |
| 27. #19149601 | C22 | semidirect |
| 28. #19149601 | C22 | semidirect |
| 31. C22⋊C8×C173 | C22 | semidirect |
| 32. C22⋊C8×C173 | C22 | semidirect |
| 125. C173 | #3094 | semidirect |
| 134. #407 | D173 | semidirect |
| 157. C22⋊C8 | C2×D173 | semidirect |
| 158. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149653 | 2 |
| C2×#19149638 | 2 |
| #26011816 | 2 |
| #26011810 | 2 |
| #26011805 | 2 |
| #26011533 | 2 |
| #26011497 | 2 |
| #407×C173 | 2 |
| #3094 | 173 |