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. C13×#535 | C2 | semidirect |
| 2. C2×#88205 | C2 | semidirect |
| 3. C2×#88204 | C2 | semidirect |
| 4. C22×#6105 | C2 | semidirect |
| 5. C2×#88186 | C2 | semidirect |
| 6. #11719231 | C2 | semidirect |
| 7. #11718737 | C2 | semidirect |
| 8. #11718735 | C2 | semidirect |
| 9. #11718721 | C2 | semidirect |
| 10. #11718720 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 23. C2×#6107 | C22 | semidirect |
| 24. C2×#6107 | C22 | semidirect |
| 25. C2×#6106 | C22 | semidirect |
| 30. C2×#6105 | C22 | semidirect |
| 31. C2×#6105 | C22 | semidirect |
| 34. C2×#6104 | C22 | semidirect |
| 39. #88129 | C22 | semidirect |
| 40. #88123 | C22 | semidirect |
| 41. #88043 | C22 | semidirect |
| 42. C4×#1055 | C22 | semidirect |
| 83. #6099 | D4 | semidirect |
| 84. C2×#1055 | D4 | semidirect |
| 131. #535 | 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 |
|---|---|
| C13×#535 | 2 |
| C2×#88205 | 2 |
| C2×#88204 | 2 |
| C22×#6105 | 2 |
| C2×#88186 | 2 |
| #11719231 | 2 |
| #11718737 | 2 |
| #11718735 | 2 |
| #11718721 | 2 |
| #11718720 | 2 |
| #11718658 | 2 |
| #3154 | 13 |