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. Q8×Dic26 | C2 | semidirect |
| 3. C13×#475 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 7. #11718516 | C2 | semidirect |
| 9. #11718491 | C2 | semidirect |
| 10. #11718452 | C2 | semidirect |
| 58. #6106 | Q8 | semidirect |
| 77. Q8×C13 | C2×Q8 | semidirect |
| 95. Dic26 | SD16 | semidirect |
| 98. #1055 | C2×Q8 | semidirect |
| 106. #475 | D13 | semidirect |
| 190. C13 | Q8×SD16 | semidirect |
| 198. Q8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| Q8×Dic26 | 2 |
| C13×#475 | 2 |
| #11718740 | 2 |
| C4×#6106 | 2 |
| #11718531 | 2 |
| #11718516 | 2 |
| #11718503 | 2 |
| #11718491 | 2 |
| #11718452 | 2 |
| #11718449 | 2 |
| Q8×SD16 | 13 |