Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 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×#475 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. C4×#6106 | C2 | semidirect |
| 6. #11718527 | C2 | semidirect |
| 7. #11718522 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718499 | C2 | semidirect |
| 10. #11718473 | C2 | semidirect |
| 11. #11718470 | C2 | semidirect |
| 100. #1055 | #41 | semidirect |
| 106. #475 | D13 | semidirect |
| 196. C13 | #3353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719431 | 2 |
| #11719289 | 2 |
| C13×#475 | 2 |
| #11718739 | 2 |
| C4×#6106 | 2 |
| #11718527 | 2 |
| #11718522 | 2 |
| #11718507 | 2 |
| #11718499 | 2 |
| #11718473 | 2 |
| #11718470 | 2 |
| #3353 | 13 |