Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26012025 | C2 | semidirect |
| 2. #26011873 | C2 | semidirect |
| 3. #26011845 | C2 | semidirect |
| 4. #26011710 | C2 | semidirect |
| 5. #26011703 | C2 | semidirect |
| 6. #26011647 | C2 | semidirect |
| 7. #26011642 | C2 | semidirect |
| 8. #26011630 | C2 | semidirect |
| 10. #26011544 | C2 | semidirect |
| 11. C2×#124×C173 | C2 | semidirect |
| 12. C2×#14583816 | C22 | semidirect |
| 14. C2×#14583813 | C22 | semidirect |
| 17. #19149671 | C22 | semidirect |
| 18. #19149667 | C22 | semidirect |
| 22. C4×Dic346 | C22 | semidirect |
| 23. C4×D692 | C22 | semidirect |
| 26. C4⋊#13063436 | C22 | semidirect |
| 27. #19149603 | C22 | semidirect |
| 28. #19149603 | C22 | semidirect |
| 33. C4×#13063436 | C22 | semidirect |
| 143. C173 | #3211 | semidirect |
| 146. C2×#124 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012025 | 2 |
| #26011873 | 2 |
| #26011845 | 2 |
| #26011710 | 2 |
| #26011703 | 2 |
| #26011647 | 2 |
| #26011642 | 2 |
| #26011630 | 2 |
| #26011625 | 2 |
| #26011544 | 2 |
| C2×#124×C173 | 2 |
| #3211 | 173 |