Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
428 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. #11718754 | C2 | semidirect |
| 4. #11718737 | C2 | semidirect |
| 5. #11718701 | C2 | semidirect |
| 6. #11718680 | C2 | semidirect |
| 7. #11718586 | C2 | semidirect |
| 69. C2×C4×C13 | SD16 | semidirect |
| 157. C13 | #3206 | semidirect |
| 173. C2×C4 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C2×#88123 | 2 |
| #11718754 | 2 |
| #11718737 | 2 |
| #11718701 | 2 |
| #11718680 | 2 |
| #11718586 | 2 |
| #3206 | 13 |