Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
504 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 125 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×#88166 | C2 | semidirect |
| 2. #11719423 | C2 | semidirect |
| 3. C13×#493 | C2 | semidirect |
| 4. #11718819 | C2 | semidirect |
| 5. #11718818 | C2 | semidirect |
| 6. #11718736 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 8. C8×D52 | C2 | semidirect |
| 53. Dic52 | D4 | semidirect |
| 81. #493 | D13 | semidirect |
| 95. C4×C13 | #135 | semidirect |
| 152. C13 | #3287 | semidirect |
| 187. C4 | #88166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88166 | 2 |
| #11719423 | 2 |
| C13×#493 | 2 |
| #11718819 | 2 |
| #11718818 | 2 |
| #11718736 | 2 |
| C4×Dic52 | 2 |
| C8×D52 | 2 |
| #3287 | 13 |