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. C2×C13×#135 | C2 | semidirect |
| 2. #11719537 | C2 | semidirect |
| 3. C2×#88204 | C2 | semidirect |
| 4. C2×#88158 | C2 | semidirect |
| 5. #11718851 | C2 | semidirect |
| 6. #11718837 | C2 | semidirect |
| 7. #11718828 | C2 | semidirect |
| 8. #11718815 | C2 | semidirect |
| 9. C2×#88055 | C2 | semidirect |
| 54. C2×C8×C13 | D4 | semidirect |
| 66. C2×#1055 | D4 | semidirect |
| 101. C2×#135 | D13 | semidirect |
| 179. C2×C8 | C22⋊D13 | semidirect |
| 187. C13 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11719537 | 2 |
| C2×#88204 | 2 |
| C2×#88158 | 2 |
| #11718851 | 2 |
| #11718837 | 2 |
| #11718828 | 2 |
| #11718815 | 2 |
| C2×#88055 | 2 |
| #3150 | 13 |