Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 2. #11719427 | C2 | semidirect |
| 3. C13×#498 | C2 | semidirect |
| 4. #11718755 | C2 | semidirect |
| 7. #11718516 | C2 | semidirect |
| 8. #11718515 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 72. #6095 | Q8 | semidirect |
| 94. Dic26 | SD16 | semidirect |
| 95. Dic26 | C2×Q8 | semidirect |
| 97. C8×C13 | C2×Q8 | semidirect |
| 102. #498 | D13 | semidirect |
| 190. C13 | Q8×SD16 | semidirect |
| 215. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| #11719427 | 2 |
| C13×#498 | 2 |
| #11718755 | 2 |
| #11718745 | 2 |
| #11718531 | 2 |
| #11718516 | 2 |
| #11718515 | 2 |
| #11718513 | 2 |
| C4×#6095 | 2 |
| C8×Dic26 | 2 |
| Q8×SD16 | 13 |