Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719175 | C2 | semidirect |
| 3. C13×#432 | C2 | semidirect |
| 4. #11718506 | C2 | semidirect |
| 5. #11718400 | C2 | semidirect |
| 7. #11718376 | C2 | semidirect |
| 8. #11718375 | C2 | semidirect |
| 17. C2×Dic52 | C22 | semidirect |
| 24. #88123 | C22 | semidirect |
| 25. #88123 | C22 | semidirect |
| 27. C4×Dic26 | C22 | semidirect |
| 28. C13×C4⋊C8 | C22 | semidirect |
| 30. C13×#97 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 98. #432 | D13 | semidirect |
| 135. C4⋊C8 | C2×D13 | semidirect |
| 139. #97 | C2×D13 | semidirect |
| 177. C13 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| #11719175 | 2 |
| C13×#432 | 2 |
| #11718506 | 2 |
| #11718400 | 2 |
| #11718392 | 2 |
| #11718376 | 2 |
| #11718375 | 2 |
| #3215 | 13 |