Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88124 | C2 | semidirect |
| 3. C2×C4×C8×C13 | C2 | semidirect |
| 5. C2×#88056 | C2 | semidirect |
| 6. #11718358 | C2 | direct (N × H) |
| 17. #88124 | C22 | semidirect |
| 18. C4×C8×C13 | C22 | semidirect |
| 20. #88056 | C22 | semidirect |
| 64. C2×C4×C8 | D13 | semidirect |
| 89. C4×C8 | C2×D13 | semidirect |
| 90. C2×C13 | #488 | semidirect |
| 113. C13 | C2×#488 | semidirect |
| 144. C2 | #11718358 | 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×#88124 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#88061 | 2 |
| C2×#88056 | 2 |
| #11718358 | 2 |
| C2×#488 | 13 |