Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11719476 | C2 | semidirect |
| 2. #11719471 | C2 | semidirect |
| 3. C13×#510 | C2 | semidirect |
| 4. #11718855 | C2 | semidirect |
| 5. C2×#88069 | C2 | semidirect |
| 6. #11718579 | C2 | semidirect |
| 7. D13×Q32 | C2 | semidirect |
| 8. #11718577 | C2 | semidirect |
| 9. #11718576 | C2 | semidirect |
| 10. #11718570 | C2 | semidirect |
| 11. #11718568 | C2 | semidirect |
| 113. #510 | D13 | semidirect |
| 200. C13 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719476 | 2 |
| #11719471 | 2 |
| C13×#510 | 2 |
| #11718855 | 2 |
| C2×#88069 | 2 |
| #11718579 | 2 |
| D13×Q32 | 2 |
| #11718577 | 2 |
| #11718576 | 2 |
| #11718570 | 2 |
| #11718568 | 2 |
| #3417 | 13 |