Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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. #11719524 | C2 | semidirect |
| 3. C2×#88077 | C2 | semidirect |
| 4. #11718858 | C2 | semidirect |
| 5. #11718857 | C2 | semidirect |
| 6. #11718786 | C2 | semidirect |
| 7. M16×Dic13 | C2 | semidirect |
| 9. C13×#137 | C4 | semidirect |
| 10. C13×AGL(1,ℤ/8) | C4 | semidirect |
| 14. #88202 | C22 | semidirect |
| 19. #88077 | C22 | semidirect |
| 20. #88077 | C22 | semidirect |
| 21. #88059 | C22 | semidirect |
| 22. #88055 | C22 | semidirect |
| 23. C8×Dic13 | C22 | semidirect |
| 34. C13×Q16 | C2×C4 | semidirect |
| 35. C13×SD16 | C2×C4 | semidirect |
| 36. C13×D8 | C2×C4 | semidirect |
| 90. #137 | Dic13 | semidirect |
| 91. AGL(1,ℤ/8) | Dic13 | semidirect |
| 119. Q16 | C2×Dic13 | semidirect |
| 120. SD16 | C2×Dic13 | semidirect |
| 121. D8 | C2×Dic13 | semidirect |
| 134. C13 | #2956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#575 | 2 |
| #11719524 | 2 |
| C2×#88077 | 2 |
| #11718858 | 2 |
| #11718857 | 2 |
| #11718786 | 2 |
| M16×Dic13 | 2 |
| #2956 | 13 |