Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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. C2×#88107 | C2 | semidirect |
| 3. #11718226 | C2 | semidirect |
| 4. #11718225 | C2 | semidirect |
| 5. C2×#6127 | C4 | semidirect |
| 8. C13×#117 | C4 | semidirect |
| 11. #88129 | C4 | semidirect |
| 13. #88128 | C4 | semidirect |
| 26. C2×D52 | C2×C4 | semidirect |
| 30. C2×Dic26 | C2×C4 | semidirect |
| 35. C42×C13 | C2×C4 | semidirect |
| 36. C42×C13 | C2×C4 | semidirect |
| 93. #117 | #261 | semidirect |
| 123. C42 | C2×#261 | semidirect |
| 124. C42 | C2×#261 | semidirect |
| 125. C13 | #2127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719230 | 2 |
| C2×#88107 | 2 |
| #11718226 | 2 |
| #11718225 | 2 |
| #2127 | 13 |