Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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×#520 | C2 | semidirect |
| 3. #11718895 | C2 | semidirect |
| 4. #11718664 | C2 | semidirect |
| 5. #11718663 | C2 | semidirect |
| 6. #11718657 | C2 | semidirect |
| 7. #11718656 | C2 | semidirect |
| 8. #11718631 | C2 | semidirect |
| 9. #11718628 | C2 | semidirect |
| 10. #11718627 | C2 | semidirect |
| 11. C2×#88047 | C2 | semidirect |
| 110. #520 | D13 | semidirect |
| 210. C13 | #3098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#520 | 2 |
| #11719538 | 2 |
| #11718895 | 2 |
| #11718664 | 2 |
| #11718663 | 2 |
| #11718657 | 2 |
| #11718656 | 2 |
| #11718631 | 2 |
| #11718628 | 2 |
| #11718627 | 2 |
| C2×#88047 | 2 |
| #3098 | 13 |