Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
466 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 145 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×#568 | C2 | semidirect |
| 2. #11719527 | C2 | semidirect |
| 3. C2×#88203 | C2 | semidirect |
| 4. C2×#88162 | C2 | semidirect |
| 5. #11718803 | C2 | semidirect |
| 6. #11718802 | C2 | semidirect |
| 7. #11718793 | C2 | semidirect |
| 8. C2×#88063 | C2 | semidirect |
| 9. #11718786 | C2 | semidirect |
| 14. C13×#131 | C22 | semidirect |
| 18. #88205 | C22 | semidirect |
| 22. #88203 | C22 | semidirect |
| 31. C2×D104 | C22 | semidirect |
| 32. C2×#6095 | C22 | semidirect |
| 33. #88064 | C22 | semidirect |
| 34. #88063 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88059 | C22 | semidirect |
| 126. #568 | D13 | semidirect |
| 167. #131 | C2×D13 | semidirect |
| 230. C13 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#568 | 2 |
| #11719527 | 2 |
| C2×#88203 | 2 |
| C2×#88162 | 2 |
| #11718803 | 2 |
| #11718802 | 2 |
| #11718793 | 2 |
| C2×#88063 | 2 |
| #11718786 | 2 |
| #3068 | 13 |