Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
958 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 449 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D73 |
| commutator, socle | C22×C73 | C25 |
| Fitting | H(3,𝔽4)×C73 | C2 |
| hypercenter | H(3,𝔽4) | D73 |
| hypocenter | C73 | #3568 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989337 | C2 | semidirect |
| 2. #17989306 | C2 | semidirect |
| 3. #17989268 | C2 | semidirect |
| 4. #17989201 | C2 | semidirect |
| 5. #17989172 | C2 | semidirect |
| 6. #17989116 | C2 | semidirect |
| 7. H(3,𝔽4)×C73 | C2 | semidirect |
| 8. #14556589 | C22 | semidirect |
| 9. #14556585 | C22 | semidirect |
| 10. #14556584 | C22 | semidirect |
| 11. #14556584 | C22 | semidirect |
| 12. #14556584 | C22 | semidirect |
| 13. #14556584 | C22 | semidirect |
| 14. #14556583 | C22 | semidirect |
| 16. #14556577 | C22 | semidirect |
| 17. #14556573 | C22 | semidirect |
| 20. #14556568 | C22 | semidirect |
| 21. #14556568 | C22 | semidirect |
| 22. #14556568 | C22 | semidirect |
| 23. #14556567 | C22 | semidirect |
| 26. #14556560 | C22 | semidirect |
| 27. Q8×Dic73 | C22 | semidirect |
| 28. C4×Dic146 | C22 | semidirect |
| 31. #14556551 | C22 | semidirect |
| 32. #14556547 | C22 | semidirect |
| 33. #14556547 | C22 | semidirect |
| 34. C2×C22⋊Dic73 | C22 | semidirect |
| 35. C42×D73 | C22 | semidirect |
| 101. C73 | #3568 | semidirect |
| 103. H(3,𝔽4) | D73 | semidirect |