Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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×#19149709 | C2 | semidirect |
| 2. C2×#19149658 | C2 | semidirect |
| 3. #26011653 | C2 | semidirect |
| 4. #26011647 | C2 | semidirect |
| 5. #26011642 | C2 | semidirect |
| 6. #26011492 | C2 | semidirect |
| 7. #26011455 | C2 | semidirect |
| 9. C22×Dic346 | C22 | semidirect |
| 11. C2×#14583816 | C22 | semidirect |
| 12. C2×#14583814 | C22 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 17. #19149658 | C22 | semidirect |
| 18. C2×C4⋊Dic173 | C22 | semidirect |
| 21. #19149603 | C22 | semidirect |
| 22. #19149600 | C22 | semidirect |
| 24. C22⋊#13063436 | C22 | semidirect |
| 130. C22×C173 | #137 | semidirect |
| 146. C173 | #3007 | semidirect |
| 277. C22 | #19149709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149658 | 2 |
| #26011653 | 2 |
| #26011647 | 2 |
| #26011642 | 2 |
| #26011492 | 2 |
| #26011455 | 2 |
| C22×#41×C173 | 2 |
| #3007 | 173 |