Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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. #11719432 | C2 | semidirect |
| 2. #11719418 | C2 | semidirect |
| 3. C13×#486 | C2 | semidirect |
| 4. #11718755 | C2 | semidirect |
| 6. #11718448 | C2 | semidirect |
| 7. #11718446 | C2 | semidirect |
| 8. #11718426 | C2 | semidirect |
| 9. #11718422 | C2 | semidirect |
| 10. C4×#6095 | C2 | semidirect |
| 11. #11718340 | C2 | semidirect |
| 106. #486 | D13 | semidirect |
| 198. C13 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719432 | 2 |
| #11719418 | 2 |
| C13×#486 | 2 |
| #11718755 | 2 |
| #11718733 | 2 |
| #11718448 | 2 |
| #11718446 | 2 |
| #11718426 | 2 |
| #11718422 | 2 |
| C4×#6095 | 2 |
| #11718340 | 2 |
| #3373 | 13 |