Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
712 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 126 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. #13130563 | C2 | semidirect |
| 3. #13130012 | C2 | semidirect |
| 4. #13129709 | C2 | semidirect |
| 8. C2×C4×D52 | C4 | semidirect |
| 15. C4×C13×C4⋊C4 | C4 | semidirect |
| 16. #11718649 | C4 | semidirect |
| 18. #11718646 | C4 | semidirect |
| 23. #11718240 | C4 | semidirect |
| 54. (C2×#261)⋊C4 | C2×C4 | semidirect |
| 56. #88111 | C2×C4 | semidirect |
| 198. C4×C4⋊C4 | #261 | semidirect |
| 345. C13 | #8216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13130563 | 2 |
| C2×#11718240 | 2 |
| #13130012 | 2 |
| #13129709 | 2 |
| C4×#88149 | 2 |
| #8216 | 13 |