Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C2×C13×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11719530 | C2 | semidirect |
| 3. C2×#88204 | C2 | semidirect |
| 4. #11719510 | C2 | semidirect |
| 5. C22×#6105 | C2 | semidirect |
| 6. C2×#88163 | C2 | semidirect |
| 7. #11718836 | C2 | semidirect |
| 8. #11718828 | C2 | semidirect |
| 9. #11718816 | C2 | semidirect |
| 10. #11718815 | C2 | semidirect |
| 11. #11718783 | C2 | semidirect |
| 22. #88198 | C22 | semidirect |
| 23. C2×#6107 | C22 | semidirect |
| 24. C2×#6106 | C22 | semidirect |
| 28. #88190 | C22 | semidirect |
| 33. C2×#6105 | C22 | semidirect |
| 34. C2×#6104 | C22 | semidirect |
| 39. C2×Dic52 | C22 | semidirect |
| 40. C2×#6095 | C22 | semidirect |
| 41. #88055 | C22 | semidirect |
| 42. C8×Dic13 | C22 | semidirect |
| 69. C13×M16 | D4 | semidirect |
| 83. C2×#1055 | D4 | semidirect |
| 127. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 225. M16 | C22⋊D13 | semidirect |
| 236. C13 | #3154 | 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 |
| #11719530 | 2 |
| C2×#88204 | 2 |
| #11719510 | 2 |
| C22×#6105 | 2 |
| C2×#88163 | 2 |
| #11718836 | 2 |
| #11718828 | 2 |
| #11718816 | 2 |
| #11718815 | 2 |
| #11718783 | 2 |
| #3154 | 13 |