Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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×#131 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C22×D104 | C2 | semidirect |
| 4. #11718803 | C2 | direct (N × H) |
| 5. C2×#88063 | C2 | semidirect |
| 6. C2×#88059 | C2 | semidirect |
| 10. C13×#131 | C22 | semidirect |
| 16. #88203 | C22 | semidirect |
| 23. C2×D104 | C22 | semidirect |
| 24. #88063 | C22 | semidirect |
| 25. #88059 | C22 | semidirect |
| 90. C2×#131 | D13 | semidirect |
| 120. #131 | C2×D13 | semidirect |
| 131. C2×C13 | #472 | semidirect |
| 166. C13 | C2×#472 | semidirect |
| 215. C2 | #11718803 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#131 | 2 |
| C2×#88203 | 2 |
| C22×D104 | 2 |
| #11718803 | 2 |
| C2×#88063 | 2 |
| C2×#88059 | 2 |
| C2×#472 | 13 |