Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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×#533 | C2 | semidirect |
| 3. #11718752 | C2 | semidirect |
| 4. #11718751 | C2 | semidirect |
| 5. #11718745 | C2 | semidirect |
| 6. #11718744 | C2 | semidirect |
| 8. #11718706 | C2 | semidirect |
| 9. #11718691 | C2 | semidirect |
| 10. #11718687 | C2 | semidirect |
| 11. #11718587 | C2 | semidirect |
| 113. #533 | D13 | semidirect |
| 218. C13 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#533 | 2 |
| C4×#6127 | 2 |
| #11718752 | 2 |
| #11718751 | 2 |
| #11718745 | 2 |
| #11718744 | 2 |
| #11718708 | 2 |
| #11718706 | 2 |
| #11718691 | 2 |
| #11718687 | 2 |
| #11718587 | 2 |
| #3116 | 13 |