Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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×C13×#97 | C2 | semidirect |
| 4. C2×#88061 | C2 | semidirect |
| 5. #11718374 | C2 | direct (N × H) |
| 15. #88124 | C22 | semidirect |
| 16. C13×#97 | C22 | semidirect |
| 17. #88061 | C22 | semidirect |
| 54. C2×#97 | D13 | semidirect |
| 76. #97 | C2×D13 | semidirect |
| 77. C2×C13 | #490 | semidirect |
| 97. C13 | C2×#490 | semidirect |
| 124. C2 | #11718374 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88128 | 2 |
| C2×#88124 | 2 |
| C2×C13×#97 | 2 |
| C2×#88061 | 2 |
| #11718374 | 2 |
| C2×#490 | 13 |