Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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×C4×Dic26 | C2 | semidirect |
| 3. C13×#432 | C2 | semidirect |
| 4. #11718506 | C2 | semidirect |
| 5. #11718490 | C2 | semidirect |
| 6. #11718400 | C2 | semidirect |
| 9. #11718383 | C2 | semidirect |
| 10. #11718377 | C2 | semidirect |
| 11. #11718371 | C2 | semidirect |
| 119. #432 | D13 | semidirect |
| 212. C13 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719184 | 2 |
| C2×C4×Dic26 | 2 |
| C13×#432 | 2 |
| #11718506 | 2 |
| #11718490 | 2 |
| #11718400 | 2 |
| #11718399 | 2 |
| #11718396 | 2 |
| #11718383 | 2 |
| #11718377 | 2 |
| #11718371 | 2 |
| #3117 | 13 |