Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149705 | C2 | semidirect |
| 3. C2×#19149699 | C2 | semidirect |
| 4. C22×#14583814 | C2 | semidirect |
| 5. #26012067 | C2 | semidirect |
| 6. #26011886 | C2 | semidirect |
| 7. #26011878 | C2 | semidirect |
| 8. #26011873 | C2 | semidirect |
| 9. #26011863 | C2 | semidirect |
| 10. #26011447 | C2 | semidirect |
| 11. #535×C173 | C2 | semidirect |
| 17. C2×#14583816 | C22 | semidirect |
| 18. C2×#14583816 | C22 | semidirect |
| 23. C2×#14583814 | C22 | semidirect |
| 24. C2×#14583814 | C22 | semidirect |
| 25. C2×#14583813 | C22 | semidirect |
| 27. C2×#14583811 | C22 | semidirect |
| 30. #19149679 | C22 | semidirect |
| 31. #19149667 | C22 | semidirect |
| 34. #19149590 | C22 | semidirect |
| 35. C4×#13063436 | C22 | semidirect |
| 64. #14583810 | D4 | semidirect |
| 65. C2×#13063436 | D4 | semidirect |
| 148. C173 | #3154 | semidirect |
| 155. #535 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149709 | 2 |
| C2×#19149705 | 2 |
| C2×#19149699 | 2 |
| C22×#14583814 | 2 |
| #26012067 | 2 |
| #26011886 | 2 |
| #26011878 | 2 |
| #26011873 | 2 |
| #26011863 | 2 |
| #26011447 | 2 |
| #535×C173 | 2 |
| #3154 | 173 |