Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
3798 conjugacy classes of subgroups; only the 824 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 824 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. #13131380 | C2 | direct (N × H) |
| 2. C2×#11719150 | C2 | semidirect |
| 3. C2×#11719061 | C2 | semidirect |
| 8. C2×C13×#127 | C4 | semidirect |
| 9. C2×#88194 | C4 | semidirect |
| 10. D13×#127 | C4 | semidirect |
| 12. C2×#88128 | C4 | semidirect |
| 14. #11719150 | C22 | semidirect |
| 16. #11719061 | C22 | semidirect |
| 21. C22×D4×C13 | C2×C4 | semidirect |
| 22. C22×C22⋊D13 | C2×C4 | semidirect |
| 25. C2×D4×D13 | C2×C4 | semidirect |
| 27. C22×D52 | C2×C4 | semidirect |
| 31. C13×#127 | C2×C4 | semidirect |
| 32. C2×C42×C13 | C2×C4 | semidirect |
| 33. #88194 | C2×C4 | semidirect |
| 34. C2×C4×Dic13 | C2×C4 | semidirect |
| 35. #88128 | C2×C4 | semidirect |
| 36. C42×D13 | C2×C4 | semidirect |
| 52. C2×D4×C13 | C22×C4 | semidirect |
| 55. C2×C22⋊D13 | C22×C4 | semidirect |
| 61. C2×D52 | C22×C4 | semidirect |
| 66. C42×C13 | C22×C4 | semidirect |
| 67. C4×Dic13 | C22×C4 | semidirect |
| 103. C2×#127 | #261 | semidirect |
| 131. C22×D4 | C2×#261 | semidirect |
| 138. #127 | C2×#261 | semidirect |
| 144. C2×C42 | C2×#261 | semidirect |
| 147. C2×C13 | #2380 | semidirect |
| 150. D13 | #2380 | semidirect |
| 167. C2×D4 | C22×#261 | semidirect |
| 179. C42 | C22×#261 | semidirect |
| 180. C13 | C2×#2380 | semidirect |
| 225. C2 | #13131380 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131380 | 2 |
| C2×#11719150 | 2 |
| C2×#11719061 | 2 |
| C2×D13×#127 | 2 |
| C2×#2380 | 13 |