Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#88162 | C2 | semidirect |
| 2. C22×D104 | C2 | semidirect |
| 3. #11719230 | C2 | semidirect |
| 4. #11719226 | C2 | semidirect |
| 5. C13×#424 | C2 | semidirect |
| 6. #11718792 | C2 | semidirect |
| 7. #11718774 | C2 | semidirect |
| 8. #11718505 | C2 | semidirect |
| 9. #11718504 | C2 | semidirect |
| 20. C2×D104 | C22 | semidirect |
| 21. C2×#6095 | C22 | semidirect |
| 26. #88129 | C22 | semidirect |
| 27. #88128 | C22 | semidirect |
| 28. C4×D52 | C22 | semidirect |
| 29. C13×C4⋊C8 | C22 | semidirect |
| 30. #88061 | C22 | semidirect |
| 31. #88061 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 45. C2×D52 | D4 | semidirect |
| 105. #424 | D13 | semidirect |
| 144. C4⋊C8 | C2×D13 | semidirect |
| 188. C13 | #3041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88162 | 2 |
| C22×D104 | 2 |
| #11719230 | 2 |
| #11719226 | 2 |
| C13×#424 | 2 |
| #11718792 | 2 |
| #11718774 | 2 |
| #11718505 | 2 |
| #11718504 | 2 |
| #3041 | 13 |