Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 97 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×#88123 | C2 | semidirect |
| 4. C2×#88050 | C2 | semidirect |
| 5. #11718116 | C2 | semidirect |
| 54. C2×C4×C13 | SD16 | semidirect |
| 128. C13 | #2013 | semidirect |
| 148. C2×C4 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6105 | 2 |
| C2×#88123 | 2 |
| C13×#390 | 2 |
| C2×#88050 | 2 |
| #11718116 | 2 |
| #2013 | 13 |