Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 3. #11718267 | C2 | semidirect |
| 8. #88237 | C4 | semidirect |
| 11. C2×C4×#261 | C4 | semidirect |
| 12. C2×C13×M16 | C4 | semidirect |
| 13. C2×#6099 | C4 | semidirect |
| 17. C2×C8×D13 | C4 | semidirect |
| 35. C4×#261 | C2×C4 | semidirect |
| 37. C2×C8×C13 | C2×C4 | semidirect |
| 39. C2×#1055 | C2×C4 | semidirect |
| 97. C2×M16 | #261 | semidirect |
| 111. D13 | H(3,ℤ/4) | semidirect |
| 130. C2×C8 | C2×#261 | semidirect |
| 137. C13 | C2×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88237 | 2 |
| C2×M16×D13 | 2 |
| #11718267 | 2 |
| C2×H(3,ℤ/4) | 13 |