Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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×C13×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11719538 | C2 | semidirect |
| 3. #11719510 | C2 | semidirect |
| 4. C2×#88161 | C2 | semidirect |
| 5. #11718894 | C2 | semidirect |
| 6. C2×#88072 | C2 | semidirect |
| 7. #11718835 | C2 | semidirect |
| 8. #11718832 | C2 | semidirect |
| 9. #11718820 | C2 | semidirect |
| 10. #11718818 | C2 | semidirect |
| 11. #11718782 | C2 | semidirect |
| 20. #88200 | C22 | semidirect |
| 25. #88192 | C22 | semidirect |
| 33. C2×#6094 | C22 | semidirect |
| 34. C2×C8×D13 | C22 | semidirect |
| 35. #88075 | C22 | semidirect |
| 36. #88075 | C22 | semidirect |
| 39. #88072 | C22 | semidirect |
| 40. #88072 | C22 | semidirect |
| 41. #88058 | C22 | semidirect |
| 42. #88057 | C22 | semidirect |
| 67. C13×M16 | D4 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 219. M16 | C22⋊D13 | semidirect |
| 236. C13 | #3062 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11719538 | 2 |
| #11719510 | 2 |
| C2×#88161 | 2 |
| #11718894 | 2 |
| C2×#88072 | 2 |
| #11718835 | 2 |
| #11718832 | 2 |
| #11718820 | 2 |
| #11718818 | 2 |
| #11718782 | 2 |
| #3062 | 13 |