Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
758 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 758 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. C22×#6129 | C2 | semidirect |
| 2. C2×C13×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #11719533 | C2 | semidirect |
| 4. C2×#88205 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. #11718834 | C2 | semidirect |
| 7. #11718819 | C2 | semidirect |
| 8. #11718787 | C2 | semidirect |
| 9. #11718781 | C2 | semidirect |
| 21. C2×C13×SD16 | C22 | semidirect |
| 22. C2×C13×D8 | C22 | semidirect |
| 25. #88200 | C22 | semidirect |
| 26. C2×#6107 | C22 | semidirect |
| 27. #88192 | C22 | semidirect |
| 30. C2×#6105 | C22 | semidirect |
| 34. #88072 | C22 | semidirect |
| 35. #88060 | C22 | semidirect |
| 36. #88056 | C22 | semidirect |
| 45. C2×D4×C13 | D4 | semidirect |
| 66. C2×Dic26 | D4 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 163. C2×SD16 | C2×D13 | semidirect |
| 164. C2×D8 | C2×D13 | semidirect |
| 200. C2×D4 | C22⋊D13 | semidirect |
| 227. C13 | #3005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6129 | 2 |
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11719533 | 2 |
| C2×#88205 | 2 |
| #11718876 | 2 |
| #11718834 | 2 |
| #11718819 | 2 |
| #11718787 | 2 |
| #11718781 | 2 |
| #3005 | 13 |