Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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×#536 | C2 | semidirect |
| 2. C2×#88205 | C2 | semidirect |
| 4. C22×#6107 | C2 | semidirect |
| 5. C2×#88196 | C2 | semidirect |
| 6. #11719231 | C2 | semidirect |
| 7. #11718753 | C2 | semidirect |
| 8. #11718747 | C2 | semidirect |
| 9. #11718721 | C2 | semidirect |
| 10. #11718720 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 129. #536 | D13 | semidirect |
| 231. C13 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#536 | 2 |
| C2×#88205 | 2 |
| C2×#88204 | 2 |
| C22×#6107 | 2 |
| C2×#88196 | 2 |
| #11719231 | 2 |
| #11718753 | 2 |
| #11718747 | 2 |
| #11718721 | 2 |
| #11718720 | 2 |
| #11718658 | 2 |
| #3156 | 13 |