Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 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. C2×#88205 | C2 | semidirect |
| 4. C2×#88163 | C2 | semidirect |
| 5. #11718804 | C2 | semidirect |
| 6. #11718802 | C2 | semidirect |
| 7. C2×#88064 | C2 | semidirect |
| 8. #11718793 | C2 | semidirect |
| 9. #11718786 | C2 | semidirect |
| 31. C2×Dic52 | C22 | semidirect |
| 32. C2×#6095 | C22 | semidirect |
| 33. #88064 | C22 | semidirect |
| 34. #88064 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88059 | C22 | semidirect |
| 125. #568 | D13 | semidirect |
| 225. C13 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#568 | 2 |
| C2×#88205 | 2 |
| #11719527 | 2 |
| C2×#88163 | 2 |
| #11718804 | 2 |
| #11718802 | 2 |
| C2×#88064 | 2 |
| #11718793 | 2 |
| #11718786 | 2 |
| #3069 | 13 |