Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#88178 | C2 | semidirect |
| 3. C13×#407 | C2 | semidirect |
| 4. #11718795 | C2 | semidirect |
| 5. #11718399 | C2 | semidirect |
| 6. #11718397 | C2 | semidirect |
| 7. #11718392 | C2 | semidirect |
| 8. #11718383 | C2 | semidirect |
| 12. C22×Dic26 | C22 | semidirect |
| 13. C2×C13×M16 | C22 | semidirect |
| 21. C2×C4⋊Dic13 | C22 | semidirect |
| 25. #88178 | C22 | semidirect |
| 27. C2×#6095 | C22 | semidirect |
| 29. C13×C22⋊C8 | C22 | semidirect |
| 30. #88061 | C22 | semidirect |
| 31. #88058 | C22 | semidirect |
| 32. #88056 | C22 | semidirect |
| 108. #407 | D13 | semidirect |
| 136. C2×M16 | C2×D13 | semidirect |
| 154. C22⋊C8 | C2×D13 | semidirect |
| 196. C13 | #3193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88184 | 2 |
| C2×#88178 | 2 |
| C13×#407 | 2 |
| #11718795 | 2 |
| #11718399 | 2 |
| #11718397 | 2 |
| #11718392 | 2 |
| #11718383 | 2 |
| #3193 | 13 |