Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C13×#532 | C2 | semidirect |
| 2. C2×#88204 | C2 | semidirect |
| 3. #11719182 | C2 | semidirect |
| 4. #11718747 | C2 | semidirect |
| 5. #11718735 | C2 | semidirect |
| 6. #11718721 | C2 | semidirect |
| 7. #11718719 | C2 | semidirect |
| 8. C2×#88043 | C2 | semidirect |
| 55. C2×#1055 | D4 | semidirect |
| 82. #532 | D13 | semidirect |
| 154. C13 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#532 | 2 |
| C2×#88204 | 2 |
| #11719182 | 2 |
| #11718747 | 2 |
| #11718735 | 2 |
| #11718721 | 2 |
| #11718719 | 2 |
| C2×#88043 | 2 |
| #3150 | 13 |