Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
352 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 115 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. #11719289 | C2 | semidirect |
| 3. C13×#477 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. C4×#6106 | C2 | semidirect |
| 6. #11718546 | C2 | semidirect |
| 7. #11718541 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718495 | C2 | semidirect |
| 10. #11718475 | C2 | semidirect |
| 11. #11718468 | C2 | semidirect |
| 104. #477 | D13 | semidirect |
| 193. C13 | #3340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719439 | 2 |
| #11719289 | 2 |
| C13×#477 | 2 |
| #11718740 | 2 |
| C4×#6106 | 2 |
| #11718546 | 2 |
| #11718541 | 2 |
| #11718507 | 2 |
| #11718495 | 2 |
| #11718475 | 2 |
| #11718468 | 2 |
| #3340 | 13 |