Finite Group DatabasebetaFinite Group DatabasebetaOrder 9344.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 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 | C2 | D4×C22⋊D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #576×C73 | C2 |
| socle | C2×C73 | D42 |
| hypercenter | #576 | D73 |
| hypocenter | C73 | #3292 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #576 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17989390 | C2 | semidirect |
| 2. #17989389 | C2 | semidirect |
| 3. #17988962 | C2 | semidirect |
| 4. #17988857 | C2 | semidirect |
| 5. #17988855 | C2 | semidirect |
| 6. #17988854 | C2 | semidirect |
| 7. #17988755 | C2 | semidirect |
| 8. #17988753 | C2 | semidirect |
| 9. #17988704 | C2 | semidirect |
| 10. #17988702 | C2 | semidirect |
| 11. #576×C73 | C2 | semidirect |
| 12. #14556637 | C22 | semidirect |
| 15. #14556617 | C22 | semidirect |
| 17. #14556616 | C22 | semidirect |
| 18. #14556616 | C22 | semidirect |
| 22. C2×D584 | C22 | semidirect |
| 24. C2×#11924013 | C22 | semidirect |
| 26. #14556598 | C22 | semidirect |
| 27. #14556597 | C22 | semidirect |
| 28. #14556587 | C22 | semidirect |
| 29. #14556527 | C22 | semidirect |
| 30. #14556526 | C22 | semidirect |
| 31. #14556518 | C22 | semidirect |
| 32. #14556518 | C22 | semidirect |
| 33. #14556517 | C22 | semidirect |
| 34. #14556508 | C22 | semidirect |
| 35. #14556507 | C22 | semidirect |
| 36. C8×Dic73 | C22 | semidirect |
| 37. H(5,𝔽2)×C73 | C22 | semidirect |
| 39. AGL(1,ℤ/8)×C73 | C22 | semidirect |
| 43. C2×D8×C73 | C22 | semidirect |
| 44. #131×C73 | C22 | semidirect |
| 53. #11924018 | D4 | semidirect |
| 55. #11924016 | D4 | semidirect |
| 58. #11924015 | D4 | semidirect |
| 66. #11924013 | D4 | semidirect |
| 83. Q16×C73 | D4 | semidirect |
| 85. SD16×C73 | D4 | semidirect |
| 89. D8×C73 | D4 | semidirect |
| 154. C73 | #3292 | semidirect |
| 157. #576 | D73 | semidirect |
| 167. H(5,𝔽2) | C2×D73 | semidirect |
| 175. AGL(1,ℤ/8) | C2×D73 | semidirect |
| 186. C2×D8 | C2×D73 | semidirect |
| 189. #131 | C2×D73 | semidirect |
| 216. Q16 | C22⋊D73 | semidirect |
| 223. SD16 | C22⋊D73 | semidirect |
| 235. D8 | C22⋊D73 | semidirect |