Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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×#476 | C2 | semidirect |
| 4. #11718752 | C2 | semidirect |
| 5. #11718680 | C2 | semidirect |
| 6. #11718528 | C2 | semidirect |
| 7. #11718514 | C2 | semidirect |
| 8. #11718510 | C2 | semidirect |
| 9. #11718496 | C2 | semidirect |
| 11. #11718418 | C2 | semidirect |
| 117. #476 | D13 | semidirect |
| 218. C13 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| C4×#6129 | 2 |
| C13×#476 | 2 |
| #11718752 | 2 |
| #11718680 | 2 |
| #11718528 | 2 |
| #11718514 | 2 |
| #11718510 | 2 |
| #11718496 | 2 |
| #11718444 | 2 |
| #11718418 | 2 |
| #3116 | 13 |