Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #492×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #492 | D73 |
| hypocenter | C73 | #3208 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #492 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989142 | C2 | semidirect |
| 3. #17988961 | C2 | semidirect |
| 4. #17988934 | C2 | semidirect |
| 5. #17988933 | C2 | semidirect |
| 6. #17988785 | C2 | semidirect |
| 7. #17988736 | C2 | semidirect |
| 8. #17988638 | C2 | semidirect |
| 9. #492×C73 | C2 | semidirect |
| 13. C2×#11924015 | C22 | semidirect |
| 14. #14556591 | C22 | semidirect |
| 22. Q8×Dic73 | C22 | semidirect |
| 26. #14556520 | C22 | semidirect |
| 27. #14556513 | C22 | semidirect |
| 28. #14556512 | C22 | semidirect |
| 30. C4×#10596831 | C22 | semidirect |
| 31. C2×SD16×C73 | C22 | semidirect |
| 32. C4⋊Q8×C73 | C22 | semidirect |
| 34. C4×C8×C73 | C22 | semidirect |
| 95. C4×D73 | SD16 | semidirect |
| 125. C73 | #3208 | semidirect |
| 129. #492 | D73 | semidirect |
| 139. C2×SD16 | C2×D73 | semidirect |
| 141. C4⋊Q8 | C2×D73 | semidirect |
| 159. C4×C8 | C2×D73 | semidirect |