Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
528 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 528 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. #11719503 | C2 | semidirect |
| 3. #11718876 | C2 | semidirect |
| 4. #11718813 | C2 | semidirect |
| 5. D8×Dic13 | C2 | semidirect |
| 6. #11718767 | C2 | semidirect |
| 7. #11718762 | C2 | semidirect |
| 9. C2×C13×D8 | C4 | semidirect |
| 15. D4×Dic13 | C22 | semidirect |
| 19. #88072 | C22 | semidirect |
| 20. #88058 | C22 | semidirect |
| 21. #88057 | C22 | semidirect |
| 22. #88055 | C22 | semidirect |
| 23. C8×Dic13 | C22 | semidirect |
| 27. C2×D4×C13 | C2×C4 | semidirect |
| 31. C13×D8 | C2×C4 | semidirect |
| 32. C13×D8 | C2×C4 | semidirect |
| 33. C2×C8×C13 | C2×C4 | semidirect |
| 82. C2×D8 | Dic13 | semidirect |
| 104. C2×D4 | C2×Dic13 | semidirect |
| 108. D8 | C2×Dic13 | semidirect |
| 109. D8 | C2×Dic13 | semidirect |
| 112. C2×C8 | C2×Dic13 | semidirect |
| 122. C13 | #2948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D8 | 2 |
| #11719503 | 2 |
| #11718876 | 2 |
| #11718813 | 2 |
| D8×Dic13 | 2 |
| #11718767 | 2 |
| #11718762 | 2 |
| #2948 | 13 |