Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #11719224 | C2 | semidirect |
| 3. C13×#418 | C2 | semidirect |
| 4. C2×#88072 | C2 | semidirect |
| 5. #11718794 | C2 | semidirect |
| 6. #11718783 | C2 | semidirect |
| 7. #11718663 | C2 | semidirect |
| 8. #11718429 | C2 | semidirect |
| 9. #11718426 | C2 | semidirect |
| 10. #11718425 | C2 | semidirect |
| 11. #11718421 | C2 | semidirect |
| 24. #88144 | C22 | semidirect |
| 25. #88142 | C22 | semidirect |
| 33. #88061 | C22 | semidirect |
| 34. #88056 | C22 | semidirect |
| 35. #88055 | C22 | semidirect |
| 36. C8×Dic13 | C22 | semidirect |
| 37. #88050 | C22 | semidirect |
| 38. #88050 | C22 | semidirect |
| 39. #88049 | C22 | semidirect |
| 40. #88049 | C22 | semidirect |
| 116. #418 | D13 | semidirect |
| 212. C13 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719510 | 2 |
| #11719224 | 2 |
| C13×#418 | 2 |
| C2×#88072 | 2 |
| #11718794 | 2 |
| #11718783 | 2 |
| #11718663 | 2 |
| #11718429 | 2 |
| #11718426 | 2 |
| #11718425 | 2 |
| #11718421 | 2 |
| #3136 | 13 |