Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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. #11718226 | C2 | direct (N × H) |
| 5. C22×Dic26 | C4 | semidirect |
| 7. C2×C42×C13 | C4 | semidirect |
| 10. #88129 | C4 | semidirect |
| 27. C2×Dic26 | C2×C4 | semidirect |
| 31. C42×C13 | C2×C4 | semidirect |
| 82. C2×C42 | #261 | semidirect |
| 87. C2×C13 | #354 | semidirect |
| 110. C42 | C2×#261 | semidirect |
| 111. C13 | C2×#354 | semidirect |
| 153. C2 | #11718226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88129 | 2 |
| C2×#88107 | 2 |
| #11718226 | 2 |
| C2×#354 | 13 |