Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. C2×#19149676 | C2 | semidirect |
| 2. #26012025 | C2 | semidirect |
| 3. #26011880 | C2 | semidirect |
| 4. #26011856 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011687 | C2 | semidirect |
| 7. #26011644 | C2 | semidirect |
| 8. #26011627 | C2 | semidirect |
| 9. #432×C173 | C2 | semidirect |
| 13. C2×#14583815 | C22 | semidirect |
| 14. C2×D1384 | C22 | semidirect |
| 20. #19149671 | C22 | semidirect |
| 21. #19149667 | C22 | semidirect |
| 25. C4×Dic346 | C22 | semidirect |
| 26. C4×D692 | C22 | semidirect |
| 29. #19149601 | C22 | semidirect |
| 30. #19149601 | C22 | semidirect |
| 32. C4⋊C8×C173 | C22 | semidirect |
| 34. #97×C173 | C22 | semidirect |
| 127. C173 | #3217 | semidirect |
| 137. #432 | D173 | semidirect |
| 158. C4⋊C8 | C2×D173 | semidirect |
| 162. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| #26012025 | 2 |
| #26011880 | 2 |
| #26011856 | 2 |
| #26011692 | 2 |
| #26011687 | 2 |
| #26011644 | 2 |
| #26011627 | 2 |
| #432×C173 | 2 |
| #3217 | 173 |