Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
356 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 3. #11718752 | C2 | semidirect |
| 4. #11718739 | C2 | semidirect |
| 5. #11718712 | C2 | semidirect |
| 6. #11718705 | C2 | semidirect |
| 7. C4×#6107 | C2 | semidirect |
| 8. #11718682 | C2 | semidirect |
| 10. #11718631 | C2 | semidirect |
| 11. C2×#88047 | C2 | semidirect |
| 78. D4×C13 | Q16 | semidirect |
| 190. C13 | #3338 | semidirect |
| 198. D4 | #6107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#554 | 2 |
| #11719248 | 2 |
| #11718752 | 2 |
| #11718739 | 2 |
| #11718712 | 2 |
| #11718705 | 2 |
| C4×#6107 | 2 |
| #11718682 | 2 |
| D4×#1055 | 2 |
| #11718631 | 2 |
| C2×#88047 | 2 |
| #3338 | 13 |