Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#6095 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C2×C4×D52 | C2 | semidirect |
| 5. C2×C13×C4⋊C8 | C2 | semidirect |
| 6. C2×#88061 | C2 | semidirect |
| 7. C2×#88056 | C2 | semidirect |
| 8. #11718505 | C2 | direct (N × H) |
| 23. C2×#6095 | C22 | semidirect |
| 25. #88129 | C22 | semidirect |
| 27. C4×D52 | C22 | semidirect |
| 28. C13×C4⋊C8 | C22 | semidirect |
| 29. #88061 | C22 | semidirect |
| 30. #88056 | C22 | semidirect |
| 104. C2×C4⋊C8 | D13 | semidirect |
| 145. C4⋊C8 | C2×D13 | semidirect |
| 148. C2×C13 | #463 | semidirect |
| 188. C13 | C2×#463 | semidirect |
| 243. C2 | #11718505 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D104 | 2 |
| C22×#6095 | 2 |
| C2×#88129 | 2 |
| C2×C4×D52 | 2 |
| C2×C13×C4⋊C8 | 2 |
| C2×#88061 | 2 |
| C2×#88056 | 2 |
| #11718505 | 2 |
| C2×#463 | 13 |