Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
10894 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10894 conjugacy classes of subgroups — too many to draw. Only its 3815 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C24×D52 |
| commutator, cosocle | C4×C13 | C26 |
| Frattini | C4 | C25×D13 |
| Fitting | C13×#3573 | C2 |
| socle | C2×C13 | C24×D4 |
| hypercenter | #3573 | D13 |
| hypocenter | C13 | #63091 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #585 ◁ #3573 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129647 | C2 | semidirect |
| 2. #13129617 | C2 | semidirect |
| 3. #13129610 | C2 | semidirect |
| 4. C2×#11719457 | C2 | semidirect |
| 5. C13×#3573 | C2 | semidirect |
| 9. #11719648 | C22 | semidirect |
| 10. C2×#88256 | C22 | semidirect |
| 11. C13×#568 | C22 | semidirect |
| 12. C2×C13×#131 | C22 | semidirect |
| 13. #11719458 | C22 | semidirect |
| 14. #11719457 | C22 | semidirect |
| 15. #11719457 | C22 | semidirect |
| 16. #11719456 | C22 | semidirect |
| 17. #11719453 | C22 | semidirect |
| 18. C2×#88162 | C22 | semidirect |
| 19. C2×#88158 | C22 | semidirect |
| 20. C22×D104 | C22 | semidirect |
| 24. #88257 | C23 | semidirect |
| 26. #88256 | C23 | semidirect |
| 32. C2×#6127 | C23 | semidirect |
| 33. C22×D52 | C23 | semidirect |
| 34. C13×#131 | C23 | semidirect |
| 35. C13×#131 | C23 | semidirect |
| 36. C2×C13×M16 | C23 | semidirect |
| 37. C22×C8×C13 | C23 | semidirect |
| 38. #88163 | C23 | semidirect |
| 39. #88162 | C23 | semidirect |
| 40. C2×Dic52 | C23 | semidirect |
| 41. #88158 | C23 | semidirect |
| 42. #88158 | C23 | semidirect |
| 43. C2×D104 | C23 | semidirect |
| 44. C2×D104 | C23 | semidirect |
| 45. C2×#6095 | C23 | semidirect |
| 76. #3573 | D13 | semidirect |
| 106. #568 | C2×D13 | semidirect |
| 107. C2×#131 | C2×D13 | semidirect |
| 136. #131 | C22×D13 | semidirect |
| 137. #131 | C22×D13 | semidirect |
| 138. C2×M16 | C22×D13 | semidirect |
| 139. C22×C8 | C22×D13 | semidirect |
| 168. C13 | #63091 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129647 | 2 |
| #13129617 | 2 |
| #13129610 | 2 |
| C2×#11719457 | 2 |
| C13×#3573 | 2 |
| #63091 | 13 |