Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 6. #11718363 | C2 | semidirect |
| 7. #11718344 | C2 | semidirect |
| 8. #11718341 | C2 | semidirect |
| 31. C13×M16 | Q8 | semidirect |
| 32. C2×C8×C13 | Q8 | semidirect |
| 106. M16 | Dic26 | semidirect |
| 107. C2×C8 | Dic26 | semidirect |
| 123. C13 | #3163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719224 | 2 |
| C13×#405 | 2 |
| #11718782 | 2 |
| #11718767 | 2 |
| C2×#88057 | 2 |
| #11718363 | 2 |
| #11718344 | 2 |
| #11718341 | 2 |
| #3163 | 13 |