Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
502 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#11718573 | C2 | semidirect |
| 2. C2×D13×D16 | C2 | semidirect |
| 3. #13117147 | C2 | direct (N × H) |
| 4. C2×#11718041 | C2 | semidirect |
| 5. C2×#11718112 | C2 | semidirect |
| 6. C2×#11718111 | C2 | semidirect |
| 7. C2×#11718039 | C2 | semidirect |
| 8. C2×C13×D32 | C2 | semidirect |
| 12. C2×C13×D16 | C22 | semidirect |
| 16. #11718573 | C22 | semidirect |
| 18. D13×D16 | C22 | semidirect |
| 19. C2×Dic104 | C22 | semidirect |
| 22. C13×D32 | C22 | semidirect |
| 23. C2×C13×C32 | C22 | semidirect |
| 24. #11718112 | C22 | semidirect |
| 25. #11718111 | C22 | semidirect |
| 26. C2×#88034 | C22 | semidirect |
| 27. #11718041 | C22 | semidirect |
| 28. #11718039 | C22 | semidirect |
| 45. C13×D16 | C23 | semidirect |
| 51. Dic104 | C23 | semidirect |
| 56. C13×C32 | C23 | semidirect |
| 57. #88034 | C23 | semidirect |
| 95. C2×D32 | D13 | semidirect |
| 133. C2×D16 | C2×D13 | semidirect |
| 138. D32 | C2×D13 | semidirect |
| 141. C2×C32 | C2×D13 | semidirect |
| 178. D16 | C22×D13 | semidirect |
| 184. C32 | C22×D13 | semidirect |
| 187. C2×C13 | #2263 | semidirect |
| 221. C13 | C2×#2263 | semidirect |
| 265. C2 | #13117147 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718573 | 2 |
| C2×D13×D16 | 2 |
| #13117147 | 2 |
| C2×#11718041 | 2 |
| C2×#11718112 | 2 |
| C2×#11718111 | 2 |
| C2×#11718039 | 2 |
| C2×C13×D32 | 2 |
| C2×#2263 | 13 |