Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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. #11719395 | C2 | semidirect |
| 2. C13×#499 | C2 | semidirect |
| 3. #11718727 | C2 | semidirect |
| 4. #11718552 | C2 | semidirect |
| 5. #11718551 | C2 | semidirect |
| 7. #11718517 | C2 | semidirect |
| 9. #11718340 | C2 | semidirect |
| 59. D104 | Q8 | semidirect |
| 82. #499 | D13 | semidirect |
| 156. C13 | #3389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719395 | 2 |
| C13×#499 | 2 |
| #11718727 | 2 |
| #11718552 | 2 |
| #11718551 | 2 |
| #11718530 | 2 |
| #11718517 | 2 |
| C4×D104 | 2 |
| #11718340 | 2 |
| #3389 | 13 |