Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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. #11719272 | C2 | semidirect |
| 5. #11718681 | C2 | semidirect |
| 7. #11718515 | C2 | semidirect |
| 8. #11718453 | C2 | semidirect |
| 10. #11718342 | C2 | semidirect |
| 11. C8×Dic26 | C2 | semidirect |
| 96. Dic26 | SD16 | semidirect |
| 192. C13 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719272 | 2 |
| D4×Dic26 | 2 |
| C4×C13×SD16 | 2 |
| #11718823 | 2 |
| #11718681 | 2 |
| #11718680 | 2 |
| #11718515 | 2 |
| #11718453 | 2 |
| #11718419 | 2 |
| #11718342 | 2 |
| C8×Dic26 | 2 |
| #3359 | 13 |