Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
60570 conjugacy classes of subgroups; only the 32041 normal subgroups are shown.
This group has 60570 conjugacy classes of subgroups — too many to draw. Only its 32041 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C26×D13 |
| commutator, socle, cosocle | C2×C13 | C27 |
| Fitting | C13×H(7,𝔽2) | C2 |
| hypercenter | H(7,𝔽2) | D13 |
| hypocenter | C13 | C2×H(7,𝔽2) |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ H(7,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129647 | C2 | semidirect |
| 2. #13129646 | C2 | semidirect |
| 3. D13×#585 | C2 | semidirect |
| 4. C2×D13×H(5,𝔽2) | C2 | semidirect |
| 5. C13×H(7,𝔽2) | C2 | semidirect |
| 6. C13×#585 | C22 | semidirect |
| 7. C2×C13×H(5,𝔽2) | C22 | semidirect |
| 8. #11719652 | C22 | semidirect |
| 9. D13×2−1+4 | C22 | semidirect |
| 10. #11719650 | C22 | semidirect |
| 11. D13×H(5,𝔽2) | C22 | semidirect |
| 12. D13×H(5,𝔽2) | C22 | semidirect |
| 13. #11719648 | C22 | semidirect |
| 14. C2×#88256 | C22 | semidirect |
| 15. C2×#41×D13 | C22 | semidirect |
| 16. C2×#88251 | C22 | semidirect |
| 17. C22×D4×D13 | C22 | semidirect |
| 18. C24×D13 | C23 | semidirect |
| 19. C13×2−1+4 | C23 | semidirect |
| 20. C13×H(5,𝔽2) | C23 | semidirect |
| 21. C2×C13×#41 | C23 | semidirect |
| 22. C22×D4×C13 | C23 | semidirect |
| 23. C22×C22⋊D13 | C23 | semidirect |
| 24. #88257 | C23 | semidirect |
| 25. #88256 | C23 | semidirect |
| 26. #41×D13 | C23 | semidirect |
| 27. #41×D13 | C23 | semidirect |
| 28. #88254 | C23 | semidirect |
| 29. C2×#6131 | C23 | semidirect |
| 30. C2×Q8×D13 | C23 | semidirect |
| 31. #88251 | C23 | semidirect |
| 32. C2×#6129 | C23 | semidirect |
| 33. C2×D4×D13 | C23 | semidirect |
| 34. C2×D4×D13 | C23 | semidirect |
| 35. C2×#6127 | C23 | semidirect |
| 36. C22×D52 | C23 | semidirect |
| 37. C22×C4×D13 | C23 | semidirect |
| 39. C24×C13 | C24 | semidirect |
| 42. C23×D13 | C24 | semidirect |
| 43. C13×#41 | C24 | semidirect |
| 44. C2×Q8×C13 | C24 | semidirect |
| 45. C2×D4×C13 | C24 | semidirect |
| 46. C22×C4×C13 | C24 | semidirect |
| 47. C2×C22⋊D13 | C24 | semidirect |
| 48. C22×Dic13 | C24 | semidirect |
| 49. #6131 | C24 | semidirect |
| 51. Q8×D13 | C24 | semidirect |
| 52. #6129 | C24 | semidirect |
| 54. D4×D13 | C24 | semidirect |
| 55. #6127 | C24 | semidirect |
| 56. C2×D52 | C24 | semidirect |
| 58. C2×C4×D13 | C24 | semidirect |
| 59. C2×Dic26 | C24 | semidirect |
| 62. H(7,𝔽2) | D13 | direct (N × H) |
| 83. #585 | C2×D13 | semidirect |
| 89. C2×H(5,𝔽2) | C2×D13 | semidirect |
| 103. 2−1+4 | C22×D13 | semidirect |
| 106. H(5,𝔽2) | C22×D13 | semidirect |
| 112. C2×#41 | C22×D13 | semidirect |
| 118. C22×D4 | C22×D13 | semidirect |
| 123. D13 | H(7,𝔽2) | direct (N × H) |
| 127. C24 | C23×D13 | semidirect |
| 131. #41 | C23×D13 | semidirect |
| 135. C2×Q8 | C23×D13 | semidirect |
| 140. C2×D4 | C23×D13 | semidirect |
| 144. C22×C4 | C23×D13 | semidirect |
| 145. C13 | C2×H(7,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129647 | 2 |
| #13129646 | 2 |
| D13×#585 | 2 |
| C2×D13×H(5,𝔽2) | 2 |
| C13×H(7,𝔽2) | 2 |
| C2×H(7,𝔽2) | 13 |