Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
422 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 161 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. C13×#433 | C2 | semidirect |
| 3. #11718661 | C2 | semidirect |
| 4. #11718497 | C2 | semidirect |
| 5. #11718495 | C2 | semidirect |
| 6. #11718388 | C2 | semidirect |
| 7. D13×C22⋊C8 | C2 | semidirect |
| 8. #11718367 | C2 | semidirect |
| 9. C8×D52 | C2 | semidirect |
| 13. C2×#6094 | C22 | semidirect |
| 16. C2×C8×D13 | C22 | semidirect |
| 23. C13×C4⋊C8 | C22 | semidirect |
| 25. C13×#97 | C22 | semidirect |
| 26. C4×C8×C13 | C22 | semidirect |
| 30. #88060 | C22 | semidirect |
| 31. #88060 | C22 | semidirect |
| 32. C4⋊#1055 | C22 | semidirect |
| 33. #88043 | C22 | semidirect |
| 34. C4×#1055 | C22 | semidirect |
| 100. #433 | D13 | semidirect |
| 133. C4⋊C8 | C2×D13 | semidirect |
| 141. #97 | C2×D13 | semidirect |
| 143. C4×C8 | C2×D13 | semidirect |
| 180. C13 | #2977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719229 | 2 |
| C13×#433 | 2 |
| #11718661 | 2 |
| #11718497 | 2 |
| #11718495 | 2 |
| #11718388 | 2 |
| D13×C22⋊C8 | 2 |
| #11718367 | 2 |
| C8×D52 | 2 |
| #2977 | 13 |