Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 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 |
|---|---|---|
| 1. #11719248 | C2 | semidirect |
| 4. #11718669 | C2 | semidirect |
| 5. #11718539 | C2 | semidirect |
| 6. #11718427 | C2 | semidirect |
| 7. #11718343 | C2 | semidirect |
| 8. C8×Dic26 | C2 | semidirect |
| 33. C13×D8 | Q8 | semidirect |
| 114. D8 | Dic26 | semidirect |
| 129. C13 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719248 | 2 |
| C4×C13×D8 | 2 |
| D8×Dic13 | 2 |
| #11718669 | 2 |
| #11718539 | 2 |
| #11718427 | 2 |
| #11718343 | 2 |
| C8×Dic26 | 2 |
| #3380 | 13 |