Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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 | #490×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #490 | D73 |
| hypocenter | C73 | #3222 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #490 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989200 | C2 | semidirect |
| 3. #17988981 | C2 | semidirect |
| 4. #17988959 | C2 | semidirect |
| 5. #17988944 | C2 | semidirect |
| 6. #17988808 | C2 | semidirect |
| 7. #17988786 | C2 | semidirect |
| 8. #17988750 | C2 | semidirect |
| 9. #17988739 | C2 | semidirect |
| 10. #17988649 | C2 | semidirect |
| 11. #490×C73 | C2 | semidirect |
| 14. C2×Dic292 | C22 | semidirect |
| 17. C2×#11924016 | C22 | semidirect |
| 18. #14556591 | C22 | semidirect |
| 27. #14556556 | C22 | semidirect |
| 29. #14556520 | C22 | semidirect |
| 30. #14556514 | C22 | semidirect |
| 33. C4×#10596831 | C22 | semidirect |
| 35. #125×C73 | C22 | semidirect |
| 37. #102×C73 | C22 | semidirect |
| 38. #97×C73 | C22 | semidirect |
| 123. C73 | #3222 | semidirect |
| 128. #490 | D73 | semidirect |
| 146. #125 | C2×D73 | semidirect |
| 158. #102 | C2×D73 | semidirect |
| 160. #97 | C2×D73 | semidirect |