Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 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. C2×#88163 | C2 | semidirect |
| 3. D4×Dic26 | C2 | semidirect |
| 4. C13×#436 | C2 | semidirect |
| 5. #11718798 | C2 | semidirect |
| 6. #11718510 | C2 | semidirect |
| 7. #11718502 | C2 | semidirect |
| 8. #11718400 | C2 | semidirect |
| 9. #11718394 | C2 | semidirect |
| 10. #11718360 | C2 | semidirect |
| 11. C4×#6095 | C2 | semidirect |
| 81. #6095 | D4 | semidirect |
| 123. #436 | D13 | semidirect |
| 133. C4×C13 | #137 | semidirect |
| 216. C13 | #3276 | semidirect |
| 261. C4 | #88163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| #11719256 | 2 |
| D4×Dic26 | 2 |
| C13×#436 | 2 |
| #11718798 | 2 |
| #11718510 | 2 |
| #11718502 | 2 |
| #11718400 | 2 |
| #11718394 | 2 |
| #11718360 | 2 |
| C4×#6095 | 2 |
| #3276 | 13 |