Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
202 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 56 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. Q32×#261 | C2 | semidirect |
| 3. #13129998 | C2 | semidirect |
| 4. #13129986 | C2 | semidirect |
| 6. C32×#261 | C2 | semidirect |
| 18. C13×SD64 | C4 | semidirect |
| 19. #11718113 | C4 | semidirect |
| 20. #11718112 | C4 | semidirect |
| 21. #11718041 | C4 | semidirect |
| 33. C13×Q32 | C2×C4 | semidirect |
| 37. Dic104 | C2×C4 | semidirect |
| 41. C13×C32 | C2×C4 | semidirect |
| 42. #88034 | C2×C4 | semidirect |
| 95. SD64 | #261 | direct (N × H) |
| 111. #261 | SD64 | direct (N × H) |
| 122. Q32 | C2×#261 | semidirect |
| 135. C32 | C2×#261 | semidirect |
| 161. C13 | C4×SD64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×#261 | 2 |
| D16×#261 | 2 |
| #13129998 | 2 |
| #13129986 | 2 |
| #13129985 | 2 |
| C32×#261 | 2 |
| D13×SD64 | 2 |
| C4×SD64 | 13 |