Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#19149686 | C2 | semidirect |
| 2. #26011974 | C2 | semidirect |
| 3. #26011496 | C2 | semidirect |
| 4. #26011492 | C2 | semidirect |
| 5. #26011487 | C2 | semidirect |
| 6. C2×#19149600 | C2 | semidirect |
| 9. C2×#14583810 | C22 | semidirect |
| 10. C22×#13063436 | C22 | semidirect |
| 13. #19149638 | C22 | semidirect |
| 14. C2×C4⋊Dic173 | C22 | semidirect |
| 15. #19149603 | C22 | semidirect |
| 16. #19149603 | C22 | semidirect |
| 17. #19149600 | C22 | semidirect |
| 18. #19149600 | C22 | semidirect |
| 19. #19149600 | C22 | semidirect |
| 21. H(5,𝔽2)×C173 | C4 | semidirect |
| 41. #41×C173 | C2×C4 | semidirect |
| 49. C2×D4×C173 | C2×C4 | semidirect |
| 97. C173 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic173 | semidirect |
| 129. #41 | C2×Dic173 | semidirect |
| 137. C2×D4 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011974 | 2 |
| #26011496 | 2 |
| #26011492 | 2 |
| #26011487 | 2 |
| C2×#19149600 | 2 |
| C2×H(5,𝔽2)×C173 | 2 |
| #2897 | 173 |