Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. #11719433 | C2 | semidirect |
| 3. C13×#461 | C2 | semidirect |
| 4. #11718835 | C2 | semidirect |
| 5. #11718824 | C2 | semidirect |
| 6. #11718744 | C2 | semidirect |
| 7. #11718668 | C2 | semidirect |
| 8. #11718507 | C2 | semidirect |
| 9. #11718498 | C2 | semidirect |
| 10. #11718473 | C2 | semidirect |
| 11. #11718455 | C2 | semidirect |
| 124. #461 | D13 | semidirect |
| 224. C13 | #3254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| #11719253 | 2 |
| C13×#461 | 2 |
| #11718835 | 2 |
| #11718824 | 2 |
| #11718744 | 2 |
| #11718668 | 2 |
| #11718507 | 2 |
| #11718498 | 2 |
| #11718473 | 2 |
| #11718455 | 2 |
| #3254 | 13 |