Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8×Dic26 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 7. #11718516 | C2 | semidirect |
| 8. #11718452 | C2 | semidirect |
| 10. #11718341 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 51. C13×SD16 | Q8 | semidirect |
| 76. Q8×C13 | C2×Q8 | semidirect |
| 95. Dic26 | SD16 | direct (N × H) |
| 97. C8×C13 | C2×Q8 | semidirect |
| 168. SD16 | Dic26 | direct (N × H) |
| 190. C13 | Q8×SD16 | semidirect |
| 198. Q8 | C2×Dic26 | semidirect |
| 215. C8 | C2×Dic26 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic26 | 2 |
| D4×Dic26 | 2 |
| C4×C13×SD16 | 2 |
| SD16×Dic13 | 2 |
| #11718681 | 2 |
| #11718669 | 2 |
| #11718516 | 2 |
| #11718452 | 2 |
| #11718422 | 2 |
| #11718341 | 2 |
| C8×Dic26 | 2 |
| Q8×SD16 | 13 |