Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
406 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719437 | C2 | semidirect |
| 2. #11719423 | C2 | semidirect |
| 3. C13×#492 | C2 | semidirect |
| 4. #11718837 | C2 | semidirect |
| 5. #11718826 | C2 | semidirect |
| 6. #11718825 | C2 | semidirect |
| 7. #11718824 | C2 | semidirect |
| 8. #11718744 | C2 | semidirect |
| 9. #11718733 | C2 | semidirect |
| 10. C4×D104 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 106. C8×C13 | #41 | semidirect |
| 111. #492 | D13 | semidirect |
| 209. C13 | #3397 | semidirect |
| 239. C8 | #6129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719437 | 2 |
| #11719423 | 2 |
| C13×#492 | 2 |
| #11718837 | 2 |
| #11718826 | 2 |
| #11718825 | 2 |
| #11718824 | 2 |
| #11718744 | 2 |
| #11718733 | 2 |
| C4×D104 | 2 |
| #11718340 | 2 |
| #3397 | 13 |