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×#416 | C2 | semidirect |
| 4. #11718893 | C2 | semidirect |
| 5. C2×#88061 | C2 | semidirect |
| 6. #11718762 | C2 | semidirect |
| 7. #11718662 | C2 | semidirect |
| 8. #11718461 | C2 | semidirect |
| 9. #11718456 | C2 | semidirect |
| 10. #11718425 | C2 | semidirect |
| 11. #11718421 | C2 | semidirect |
| 24. #88144 | C22 | semidirect |
| 25. #88142 | C22 | semidirect |
| 29. C13×#103 | C22 | semidirect |
| 30. C13×#103 | C22 | semidirect |
| 31. C13×#102 | C22 | semidirect |
| 32. C13×#102 | C22 | semidirect |
| 33. #88075 | C22 | semidirect |
| 34. #88072 | C22 | semidirect |
| 37. #88055 | C22 | semidirect |
| 38. C8×Dic13 | C22 | semidirect |
| 118. #416 | D13 | semidirect |
| 159. #103 | C2×D13 | semidirect |
| 160. #103 | C2×D13 | semidirect |
| 166. #102 | C2×D13 | semidirect |
| 167. #102 | C2×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 |
|---|---|
| #11719535 | 2 |
| #11719224 | 2 |
| C13×#416 | 2 |
| #11718893 | 2 |
| C2×#88061 | 2 |
| #11718762 | 2 |
| #11718662 | 2 |
| #11718461 | 2 |
| #11718456 | 2 |
| #11718425 | 2 |
| #11718421 | 2 |
| #3136 | 13 |