Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 1. #11719433 | C2 | semidirect |
| 3. C13×#492 | C2 | semidirect |
| 4. #11718830 | C2 | semidirect |
| 5. #11718824 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. #11718731 | C2 | semidirect |
| 8. #11718355 | C2 | semidirect |
| 9. #11718346 | C2 | semidirect |
| 13. C2×C13×SD16 | C22 | semidirect |
| 14. C13×C4⋊Q8 | C22 | semidirect |
| 17. Q8×Dic13 | C22 | semidirect |
| 18. C2×#6106 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. C4×C8×C13 | C22 | semidirect |
| 30. #88072 | C22 | semidirect |
| 31. #88061 | C22 | semidirect |
| 33. #88054 | C22 | semidirect |
| 34. C4×#1055 | C22 | semidirect |
| 96. C4×D13 | SD16 | semidirect |
| 103. #492 | D13 | semidirect |
| 132. C2×SD16 | C2×D13 | semidirect |
| 134. C4⋊Q8 | C2×D13 | semidirect |
| 152. C4×C8 | C2×D13 | semidirect |
| 193. C13 | #3208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| D13×#127 | 2 |
| C13×#492 | 2 |
| #11718830 | 2 |
| #11718824 | 2 |
| #11718746 | 2 |
| #11718731 | 2 |
| #11718355 | 2 |
| #11718346 | 2 |
| #3208 | 13 |