Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C13×#137 | C2 | semidirect |
| 3. #11719521 | C2 | semidirect |
| 4. C2×#88161 | C2 | semidirect |
| 5. #11718894 | C2 | semidirect |
| 6. C2×#88075 | C2 | semidirect |
| 7. #11718850 | C2 | semidirect |
| 8. #11718849 | C2 | semidirect |
| 9. #11718835 | C2 | semidirect |
| 10. #11718832 | C2 | semidirect |
| 11. #11718782 | C2 | semidirect |
| 65. C13×M16 | D4 | semidirect |
| 119. C2×#137 | D13 | semidirect |
| 209. M16 | C22⋊D13 | semidirect |
| 228. C13 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#137 | 2 |
| #11719538 | 2 |
| #11719521 | 2 |
| C2×#88161 | 2 |
| #11718894 | 2 |
| C2×#88075 | 2 |
| #11718850 | 2 |
| #11718849 | 2 |
| #11718835 | 2 |
| #11718832 | 2 |
| #11718782 | 2 |
| #3063 | 13 |