Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #11719436 | C2 | semidirect |
| 3. C13×#492 | C2 | semidirect |
| 4. #11718835 | C2 | semidirect |
| 5. #11718832 | C2 | semidirect |
| 6. #11718825 | C2 | semidirect |
| 7. SD16×Dic13 | C2 | semidirect |
| 8. #11718743 | C2 | semidirect |
| 9. #11718732 | C2 | semidirect |
| 10. #11718350 | C2 | semidirect |
| 11. #11718344 | C2 | semidirect |
| 94. #492 | D13 | semidirect |
| 176. C13 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719436 | 2 |
| #11719424 | 2 |
| C13×#492 | 2 |
| #11718835 | 2 |
| #11718832 | 2 |
| #11718825 | 2 |
| SD16×Dic13 | 2 |
| #11718743 | 2 |
| #11718732 | 2 |
| #11718350 | 2 |
| #11718344 | 2 |
| #3174 | 13 |