Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11719224 | C2 | semidirect |
| 3. C13×#405 | C2 | semidirect |
| 4. #11718794 | C2 | semidirect |
| 5. #11718792 | C2 | semidirect |
| 6. #11718774 | C2 | semidirect |
| 7. C2×#88061 | C2 | semidirect |
| 8. #11718375 | C2 | semidirect |
| 9. #11718374 | C2 | semidirect |
| 10. #11718358 | C2 | semidirect |
| 11. #11718355 | C2 | semidirect |
| 27. #88124 | C22 | semidirect |
| 28. #88123 | C22 | semidirect |
| 29. C13×#97 | C22 | semidirect |
| 30. C4×C8×C13 | C22 | semidirect |
| 35. #88061 | C22 | semidirect |
| 36. #88061 | C22 | semidirect |
| 37. #88061 | C22 | semidirect |
| 38. #88056 | C22 | semidirect |
| 39. #88056 | C22 | semidirect |
| 40. #88056 | C22 | semidirect |
| 120. #405 | D13 | semidirect |
| 168. #97 | C2×D13 | semidirect |
| 169. C4×C8 | C2×D13 | semidirect |
| 212. C13 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719230 | 2 |
| #11719224 | 2 |
| C13×#405 | 2 |
| #11718794 | 2 |
| #11718792 | 2 |
| #11718774 | 2 |
| C2×#88061 | 2 |
| #11718375 | 2 |
| #11718374 | 2 |
| #11718358 | 2 |
| #11718355 | 2 |
| #3136 | 13 |