Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. #11719244 | C2 | semidirect |
| 4. #11718670 | C2 | semidirect |
| 5. #11718537 | C2 | semidirect |
| 6. #11718427 | C2 | semidirect |
| 7. #11718420 | C2 | semidirect |
| 8. #11718344 | C2 | semidirect |
| 9. #11718340 | C2 | semidirect |
| 41. C13×D8 | Q8 | semidirect |
| 137. D8 | Dic26 | semidirect |
| 156. C13 | #3389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719244 | 2 |
| C4×C13×D8 | 2 |
| #11718813 | 2 |
| #11718670 | 2 |
| #11718537 | 2 |
| #11718427 | 2 |
| #11718420 | 2 |
| #11718344 | 2 |
| #11718340 | 2 |
| #3389 | 13 |