Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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. C13×#518 | C2 | semidirect |
| 2. C2×#88186 | C2 | semidirect |
| 3. C22×#6104 | C2 | semidirect |
| 4. #11719230 | C2 | semidirect |
| 5. #11718677 | C2 | semidirect |
| 6. #11718676 | C2 | semidirect |
| 7. #11718663 | C2 | semidirect |
| 8. #11718662 | C2 | semidirect |
| 9. #11718660 | C2 | semidirect |
| 14. C4×D4×C13 | C22 | semidirect |
| 18. C2×#6105 | C22 | semidirect |
| 22. C2×#6104 | C22 | semidirect |
| 27. #88129 | C22 | semidirect |
| 28. #88128 | C22 | semidirect |
| 29. #88050 | C22 | semidirect |
| 30. #88049 | C22 | semidirect |
| 31. #88049 | C22 | semidirect |
| 32. C4⋊#1055 | C22 | semidirect |
| 37. C2×D4×C13 | D4 | semidirect |
| 102. #518 | D13 | semidirect |
| 140. C4×D4 | C2×D13 | semidirect |
| 168. C2×D4 | D52 | semidirect |
| 188. C13 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#518 | 2 |
| C2×#88186 | 2 |
| C22×#6104 | 2 |
| #11719230 | 2 |
| #11718677 | 2 |
| #11718676 | 2 |
| #11718663 | 2 |
| #11718662 | 2 |
| #11718660 | 2 |
| #3041 | 13 |