Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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×#554 | C2 | semidirect |
| 3. #11718752 | C2 | semidirect |
| 4. #11718749 | C2 | semidirect |
| 5. #11718710 | C2 | semidirect |
| 6. #11718708 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718688 | C2 | semidirect |
| 9. #11718673 | C2 | semidirect |
| 10. #11718628 | C2 | semidirect |
| 11. #11718627 | C2 | semidirect |
| 107. #554 | D13 | semidirect |
| 204. C13 | #3333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| #11719258 | 2 |
| #11718752 | 2 |
| #11718749 | 2 |
| #11718710 | 2 |
| #11718708 | 2 |
| C4×#6107 | 2 |
| #11718688 | 2 |
| #11718673 | 2 |
| #11718628 | 2 |
| #11718627 | 2 |
| #3333 | 13 |