Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
59186 conjugacy classes of subgroups; only the 32041 normal subgroups are shown.
This group has 59186 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 | C13×2−1+6 | C2 |
| hypercenter | 2−1+6 | D13 |
| hypocenter | C13 | C2×2−1+6 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ 2−1+6 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129649 | C2 | semidirect |
| 2. #13129648 | C2 | semidirect |
| 3. D13×#585 | C2 | semidirect |
| 4. C2×D13×2−1+4 | C2 | semidirect |
| 5. C13×2−1+6 | C2 | semidirect |
| 6. C13×#585 | C22 | semidirect |
| 7. C2×C13×2−1+4 | C22 | semidirect |
| 8. #11719652 | C22 | semidirect |
| 9. D13×2−1+4 | C22 | semidirect |
| 10. D13×2−1+4 | C22 | semidirect |
| 11. #11719650 | C22 | semidirect |
| 12. D13×H(5,𝔽2) | C22 | semidirect |
| 13. #11719648 | C22 | semidirect |
| 14. C2×#88257 | C22 | semidirect |
| 15. C2×#41×D13 | C22 | semidirect |
| 16. C2×#88254 | C22 | semidirect |
| 17. C22×Q8×D13 | C22 | semidirect |
| 18. C13×2−1+4 | C23 | semidirect |
| 19. C13×H(5,𝔽2) | C23 | semidirect |
| 20. C2×C13×#41 | C23 | semidirect |
| 21. C22×Q8×C13 | C23 | semidirect |
| 22. #88257 | C23 | semidirect |
| 23. #88256 | C23 | semidirect |
| 25. #41×D13 | C23 | semidirect |
| 26. #88254 | C23 | semidirect |
| 27. C2×#6131 | C23 | semidirect |
| 29. C2×Q8×D13 | C23 | semidirect |
| 30. #88251 | C23 | semidirect |
| 31. C2×#6129 | C23 | semidirect |
| 33. C2×#6127 | C23 | semidirect |
| 35. C22×Dic26 | C23 | semidirect |
| 57. 2−1+6 | D13 | direct (N × H) |
| 76. #585 | C2×D13 | semidirect |
| 81. C2×2−1+4 | C2×D13 | semidirect |
| 95. 2−1+4 | C22×D13 | semidirect |
| 98. H(5,𝔽2) | C22×D13 | semidirect |
| 104. C2×#41 | C22×D13 | semidirect |
| 108. C22×Q8 | C22×D13 | semidirect |
| 114. D13 | 2−1+6 | direct (N × H) |
| 133. C13 | C2×2−1+6 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129649 | 2 |
| #13129648 | 2 |
| D13×#585 | 2 |
| C2×D13×2−1+4 | 2 |
| C13×2−1+6 | 2 |
| C2×2−1+6 | 13 |