Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#88166 | C2 | semidirect |
| 2. C2×#88161 | C2 | semidirect |
| 3. #11719313 | C2 | semidirect |
| 4. C13×#469 | C2 | semidirect |
| 5. #11718820 | C2 | semidirect |
| 6. #11718798 | C2 | semidirect |
| 7. #11718702 | C2 | semidirect |
| 8. #11718529 | C2 | semidirect |
| 9. D13×#106 | C2 | semidirect |
| 10. #11718439 | C2 | semidirect |
| 11. #11718432 | C2 | semidirect |
| 80. C8×D13 | D4 | semidirect |
| 122. #469 | D13 | semidirect |
| 220. C13 | #3060 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88166 | 2 |
| C2×#88161 | 2 |
| #11719313 | 2 |
| C13×#469 | 2 |
| #11718820 | 2 |
| #11718798 | 2 |
| #11718702 | 2 |
| #11718529 | 2 |
| D13×#106 | 2 |
| #11718439 | 2 |
| #11718432 | 2 |
| #3060 | 13 |