Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. #11719517 | C2 | semidirect |
| 4. #11718886 | C2 | semidirect |
| 6. #11718825 | C2 | semidirect |
| 7. SD16×Dic13 | C2 | semidirect |
| 8. #11718767 | C2 | semidirect |
| 9. #11718762 | C2 | semidirect |
| 12. C2×C13×SD16 | C4 | semidirect |
| 18. Q8×Dic13 | C22 | semidirect |
| 26. #88075 | C22 | semidirect |
| 28. #88058 | C22 | semidirect |
| 29. #88057 | C22 | semidirect |
| 30. #88055 | C22 | semidirect |
| 31. C8×Dic13 | C22 | semidirect |
| 35. C2×Q8×C13 | C2×C4 | semidirect |
| 44. C13×SD16 | C2×C4 | semidirect |
| 45. C13×SD16 | C2×C4 | semidirect |
| 46. C2×C8×C13 | C2×C4 | semidirect |
| 111. C2×SD16 | Dic13 | semidirect |
| 138. C2×Q8 | C2×Dic13 | semidirect |
| 147. SD16 | C2×Dic13 | semidirect |
| 148. SD16 | C2×Dic13 | semidirect |
| 151. C2×C8 | C2×Dic13 | semidirect |
| 166. C13 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×SD16 | 2 |
| #11719517 | 2 |
| #11719503 | 2 |
| #11718886 | 2 |
| #11718876 | 2 |
| #11718825 | 2 |
| SD16×Dic13 | 2 |
| #11718767 | 2 |
| #11718762 | 2 |
| #2949 | 13 |