Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 340 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×#557 | C2 | semidirect |
| 5. #11718743 | C2 | semidirect |
| 6. #11718742 | C2 | semidirect |
| 9. #11718685 | C2 | semidirect |
| 10. #11718683 | C2 | semidirect |
| 11. #11718682 | C2 | semidirect |
| 98. #557 | D13 | semidirect |
| 189. C13 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#557 | 2 |
| #11719284 | 2 |
| #11718744 | 2 |
| #11718743 | 2 |
| #11718742 | 2 |
| #11718687 | 2 |
| C4×#6106 | 2 |
| #11718685 | 2 |
| #11718683 | 2 |
| #11718682 | 2 |
| #3372 | 13 |