Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #11719424 | C2 | semidirect |
| 2. C13×#493 | C2 | semidirect |
| 3. #11718820 | C2 | semidirect |
| 4. #11718818 | C2 | semidirect |
| 5. #11718813 | C2 | semidirect |
| 6. D8×Dic13 | C2 | semidirect |
| 7. #11718732 | C2 | semidirect |
| 8. #11718350 | C2 | semidirect |
| 9. #11718344 | C2 | semidirect |
| 71. #493 | D13 | semidirect |
| 134. C13 | #3176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719424 | 2 |
| C13×#493 | 2 |
| #11718820 | 2 |
| #11718818 | 2 |
| #11718813 | 2 |
| D8×Dic13 | 2 |
| #11718732 | 2 |
| #11718350 | 2 |
| #11718344 | 2 |
| #3176 | 13 |