Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #460×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #460 | D73 |
| hypocenter | C73 | #3208 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989141 | C2 | semidirect |
| 3. #17988958 | C2 | semidirect |
| 4. #17988932 | C2 | semidirect |
| 5. #17988788 | C2 | semidirect |
| 6. #17988787 | C2 | semidirect |
| 7. #17988784 | C2 | semidirect |
| 8. #17988739 | C2 | semidirect |
| 9. #17988736 | C2 | semidirect |
| 10. #17988639 | C2 | semidirect |
| 11. #460×C73 | C2 | semidirect |
| 15. C2×#11924017 | C22 | semidirect |
| 16. C2×#11924016 | C22 | semidirect |
| 17. C2×#11924015 | C22 | semidirect |
| 18. #14556590 | C22 | semidirect |
| 19. #14556589 | C22 | semidirect |
| 29. C4×Dic146 | C22 | semidirect |
| 32. C4⋊#10596831 | C22 | semidirect |
| 33. #14556513 | C22 | semidirect |
| 34. #14556512 | C22 | semidirect |
| 35. #14556511 | C22 | semidirect |
| 37. C8×Dic73 | C22 | semidirect |
| 38. C2×SD16×C73 | C22 | semidirect |
| 40. C4×Q8×C73 | C22 | semidirect |
| 41. C4⋊C8×C73 | C22 | semidirect |
| 42. #102×C73 | C22 | semidirect |
| 118. C4×D73 | SD16 | semidirect |
| 153. C73 | #3208 | semidirect |
| 161. #460 | D73 | semidirect |
| 171. C2×SD16 | C2×D73 | semidirect |
| 185. C4×Q8 | C2×D73 | semidirect |
| 189. C4⋊C8 | C2×D73 | semidirect |
| 193. #102 | C2×D73 | semidirect |