Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
516 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131766 | C2 | semidirect |
| 2. #13130969 | C2 | semidirect |
| 3. C4×#88118 | C2 | semidirect |
| 4. #13130157 | C2 | semidirect |
| 5. #13129722 | C2 | semidirect |
| 6. #13129663 | C2 | semidirect |
| 21. C13×#477 | C4 | semidirect |
| 22. #11718745 | C4 | semidirect |
| 23. #11718688 | C4 | semidirect |
| 26. #11718504 | C4 | semidirect |
| 174. D52 | #104 | semidirect |
| 197. #477 | #261 | semidirect |
| 355. C13 | #8969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131766 | 2 |
| #13130969 | 2 |
| C4×#88118 | 2 |
| #13130157 | 2 |
| #13129722 | 2 |
| #13129663 | 2 |
| #13124899 | 2 |
| #8969 | 13 |