Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19149705 | C2 | semidirect |
| 2. C2×#19149699 | C2 | semidirect |
| 3. #26011971 | C2 | semidirect |
| 4. #26011710 | C2 | semidirect |
| 5. #26011703 | C2 | semidirect |
| 6. #26011688 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011518 | C2 | semidirect |
| 9. #26011492 | C2 | semidirect |
| 10. C2×#19149600 | C2 | semidirect |
| 11. #535×C173 | C2 | semidirect |
| 15. C2×#14583816 | C22 | semidirect |
| 17. C2×#14583814 | C22 | semidirect |
| 18. C2×#14583813 | C22 | semidirect |
| 20. C2×#14583811 | C22 | semidirect |
| 23. C4×Dic346 | C22 | semidirect |
| 24. C4×D692 | C22 | semidirect |
| 29. C4⋊#13063436 | C22 | semidirect |
| 30. C4⋊#13063436 | C22 | semidirect |
| 31. #19149603 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 44. #14583826 | D4 | semidirect |
| 154. C173 | #3045 | semidirect |
| 158. #535 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C2×#19149699 | 2 |
| #26011971 | 2 |
| #26011710 | 2 |
| #26011703 | 2 |
| #26011688 | 2 |
| #26011683 | 2 |
| #26011518 | 2 |
| #26011492 | 2 |
| C2×#19149600 | 2 |
| #535×C173 | 2 |
| #3045 | 173 |