Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #11719457 | C2 | semidirect |
| 2. C13×#504 | C2 | semidirect |
| 3. #11718569 | C2 | semidirect |
| 4. #11718565 | C2 | semidirect |
| 5. C2×D208 | C2 | semidirect |
| 9. #88158 | C22 | semidirect |
| 10. C2×D104 | C22 | semidirect |
| 11. C13×M32 | C22 | semidirect |
| 12. C2×C13×C16 | C22 | semidirect |
| 13. Dic104 | C22 | semidirect |
| 14. #88040 | C22 | semidirect |
| 15. D208 | C22 | semidirect |
| 16. D208 | C22 | semidirect |
| 46. #504 | D13 | semidirect |
| 62. M32 | C2×D13 | semidirect |
| 63. C2×C16 | C2×D13 | semidirect |
| 80. C13 | #3415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719457 | 2 |
| C13×#504 | 2 |
| #11718569 | 2 |
| #11718565 | 2 |
| C2×D208 | 2 |
| #3415 | 13 |