Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
10698 conjugacy classes of subgroups; only the 3815 normal subgroups are shown.
This group has 10698 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 | #63093 |
| 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. #13129649 | C2 | semidirect |
| 2. #13129624 | C2 | semidirect |
| 3. #13129610 | C2 | semidirect |
| 4. C2×#11719458 | C2 | semidirect |
| 5. C13×#3573 | C2 | semidirect |
| 9. #11719648 | C22 | semidirect |
| 10. C2×#88257 | C22 | semidirect |
| 11. C13×#568 | C22 | semidirect |
| 12. C2×C13×#131 | C22 | semidirect |
| 13. #11719458 | C22 | semidirect |
| 14. #11719458 | C22 | semidirect |
| 15. #11719457 | C22 | semidirect |
| 16. #11719456 | C22 | semidirect |
| 17. #11719453 | C22 | semidirect |
| 18. C2×#88163 | C22 | semidirect |
| 19. C22×Dic52 | C22 | semidirect |
| 20. C2×#88158 | C22 | semidirect |
| 76. #3573 | D13 | semidirect |
| 105. #568 | C2×D13 | semidirect |
| 106. C2×#131 | C2×D13 | semidirect |
| 167. C13 | #63093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129649 | 2 |
| #13129624 | 2 |
| #13129610 | 2 |
| C2×#11719458 | 2 |
| C13×#3573 | 2 |
| #63093 | 13 |