Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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. #11719222 | C2 | semidirect |
| 5. C13×H(3,ℤ/4) | C2 | semidirect |
| 6. #11718151 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 30. C2×D52 | Q8 | semidirect |
| 33. C2×Dic26 | Q8 | semidirect |
| 88. H(3,ℤ/4) | D13 | semidirect |
| 157. C13 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719222 | 2 |
| C2×#88065 | 2 |
| #11718667 | 2 |
| #11718666 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #11718151 | 2 |
| #11718124 | 2 |
| #2031 | 13 |