Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #11719224 | C2 | semidirect |
| 5. #11718886 | C2 | semidirect |
| 6. C2×#88075 | C2 | semidirect |
| 7. #11718743 | C2 | semidirect |
| 8. #11718742 | C2 | semidirect |
| 9. #11718717 | C2 | semidirect |
| 10. #11718716 | C2 | semidirect |
| 11. #11718658 | C2 | semidirect |
| 204. C13 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#536 | 2 |
| #11719224 | 2 |
| #11718894 | 2 |
| #11718893 | 2 |
| #11718886 | 2 |
| C2×#88075 | 2 |
| #11718743 | 2 |
| #11718742 | 2 |
| #11718717 | 2 |
| #11718716 | 2 |
| #11718658 | 2 |
| #3137 | 13 |