Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #495×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #495 | D73 |
| hypocenter | C73 | #3155 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #495 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556618 | C2 | semidirect |
| 2. C2×#14556614 | C2 | semidirect |
| 3. C2×D8×D73 | C2 | semidirect |
| 4. #17989155 | C2 | semidirect |
| 5. #17988977 | C2 | semidirect |
| 6. #17988973 | C2 | semidirect |
| 7. #17988972 | C2 | semidirect |
| 8. #17988964 | C2 | semidirect |
| 9. #17988962 | C2 | semidirect |
| 10. #17988541 | C2 | semidirect |
| 11. #495×C73 | C2 | semidirect |
| 16. C2×#11924015 | C22 | semidirect |
| 17. C2×#11924015 | C22 | semidirect |
| 19. C2×D584 | C22 | semidirect |
| 20. C2×D584 | C22 | semidirect |
| 22. C2×#11924013 | C22 | semidirect |
| 26. #14556588 | C22 | semidirect |
| 27. #14556587 | C22 | semidirect |
| 28. #14556580 | C22 | semidirect |
| 32. #14556502 | C22 | semidirect |
| 33. #14556501 | C22 | semidirect |
| 34. C8×Dic73 | C22 | semidirect |
| 35. C2×Q16×C73 | C22 | semidirect |
| 36. C2×SD16×C73 | C22 | semidirect |
| 38. #124×C73 | C22 | semidirect |
| 39. C4×C8×C73 | C22 | semidirect |
| 60. #11924011 | D4 | semidirect |
| 63. C8×D73 | D4 | semidirect |
| 130. C73 | #3155 | semidirect |
| 138. #495 | D73 | semidirect |
| 146. C2×Q16 | C2×D73 | semidirect |
| 149. C2×SD16 | C2×D73 | semidirect |
| 162. #124 | C2×D73 | semidirect |
| 169. C4×C8 | C2×D73 | semidirect |