Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #11719275 | C2 | semidirect |
| 5. #11718721 | C2 | semidirect |
| 6. #11718715 | C2 | semidirect |
| 7. #11718692 | C2 | semidirect |
| 8. C4×#6107 | C2 | semidirect |
| 9. #11718685 | C2 | semidirect |
| 10. #11718680 | C2 | semidirect |
| 11. #11718679 | C2 | semidirect |
| 197. C13 | #3400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#559 | 2 |
| #11719275 | 2 |
| #11718737 | 2 |
| #11718736 | 2 |
| #11718721 | 2 |
| #11718715 | 2 |
| #11718692 | 2 |
| C4×#6107 | 2 |
| #11718685 | 2 |
| #11718680 | 2 |
| #11718679 | 2 |
| #3400 | 13 |