Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×#88142 | C2 | semidirect |
| 5. C13×#340 | C2 | semidirect |
| 6. #11718142 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 35. C2×D52 | Q8 | semidirect |
| 98. #340 | D13 | semidirect |
| 179. C13 | #2023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88142 | 2 |
| C2×#88061 | 2 |
| #11718649 | 2 |
| C2×#88049 | 2 |
| C13×#340 | 2 |
| #11718142 | 2 |
| #11718121 | 2 |
| #2023 | 13 |