Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#135 | C2 | semidirect |
| 2. #11719536 | C2 | semidirect |
| 3. C2×Q16×D13 | C2 | semidirect |
| 4. #11718900 | C2 | semidirect |
| 5. Q16×Dic13 | C2 | semidirect |
| 6. #11718831 | C2 | semidirect |
| 7. #11718827 | C2 | semidirect |
| 8. #11718818 | C2 | semidirect |
| 9. #11718816 | C2 | semidirect |
| 10. #11718777 | C2 | semidirect |
| 11. C8×C22⋊D13 | C2 | semidirect |
| 56. C13×Q16 | D4 | semidirect |
| 112. C2×#135 | D13 | semidirect |
| 132. C2×D13 | #135 | semidirect |
| 194. Q16 | C22⋊D13 | semidirect |
| 216. C13 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#135 | 2 |
| #11719536 | 2 |
| C2×Q16×D13 | 2 |
| #11718900 | 2 |
| Q16×Dic13 | 2 |
| #11718831 | 2 |
| #11718827 | 2 |
| #11718818 | 2 |
| #11718816 | 2 |
| #11718777 | 2 |
| C8×C22⋊D13 | 2 |
| #3285 | 13 |