Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×C22⋊D73 |
| commutator | C4×C73 | C25 |
| Frattini | C4 | C24×D73 |
| Fitting | #585×C73 | C2 |
| socle | C2×C73 | C23×D4 |
| hypercenter | #585 | D73 |
| hypocenter | C73 | #3586 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556638 | C2 | semidirect |
| 2. #17989402 | C2 | semidirect |
| 3. #17989398 | C2 | semidirect |
| 4. #17989385 | C2 | semidirect |
| 5. C2×#14556621 | C2 | semidirect |
| 6. #17989354 | C2 | semidirect |
| 7. #585×C73 | C2 | semidirect |
| 9. #14556638 | C22 | semidirect |
| 10. C2×#11924028 | C22 | semidirect |
| 12. C22×Dic146 | C22 | semidirect |
| 14. #14556622 | C22 | semidirect |
| 15. #14556621 | C22 | semidirect |
| 16. #14556621 | C22 | semidirect |
| 17. #14556617 | C22 | semidirect |
| 18. #14556616 | C22 | semidirect |
| 19. #14556611 | C22 | semidirect |
| 20. C2×#11924018 | C22 | semidirect |
| 21. C2×#11924016 | C22 | semidirect |
| 22. #14556598 | C22 | semidirect |
| 23. C2×#11924012 | C22 | semidirect |
| 25. 2−1+4×C73 | C22 | semidirect |
| 27. H(5,𝔽2)×C73 | C22 | semidirect |
| 113. C73 | #3586 | semidirect |
| 114. #585 | D73 | semidirect |
| 124. 2−1+4 | C2×D73 | semidirect |
| 126. H(5,𝔽2) | C2×D73 | semidirect |