Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
462 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 462 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.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | D42×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | D42 | D73 |
| hypocenter | C73 | #3295 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989294 | C2 | semidirect |
| 2. #17988933 | C2 | semidirect |
| 3. #17988903 | C2 | semidirect |
| 4. #17988877 | C2 | semidirect |
| 5. #17988814 | C2 | semidirect |
| 6. #17988784 | C2 | semidirect |
| 7. #17988738 | C2 | semidirect |
| 8. C4×#11924016 | C2 | semidirect |
| 9. D4×#10596831 | C2 | semidirect |
| 10. C2×#14556512 | C2 | semidirect |
| 13. C2×#11924016 | C22 | semidirect |
| 14. C22×#10596831 | C22 | semidirect |
| 15. #14556591 | C22 | semidirect |
| 17. #14556570 | C22 | semidirect |
| 19. C4×Dic146 | C22 | semidirect |
| 21. C2×C4⋊Dic73 | C22 | semidirect |
| 22. #14556522 | C22 | semidirect |
| 23. #14556522 | C22 | semidirect |
| 24. C4⋊#10596831 | C22 | semidirect |
| 25. #14556514 | C22 | semidirect |
| 28. #14556512 | C22 | semidirect |
| 29. #14556512 | C22 | semidirect |
| 30. #14556512 | C22 | semidirect |
| 31. C22⋊#10596831 | C22 | semidirect |
| 32. C4×#10596831 | C22 | semidirect |
| 90. D4×C73 | SD16 | semidirect |
| 137. C73 | #3295 | semidirect |
| 230. D4 | #11924016 | semidirect |