Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 85 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. #11719524 | C2 | semidirect |
| 3. C13×#413 | C2 | semidirect |
| 4. C2×#88063 | C2 | semidirect |
| 5. #11718148 | C2 | semidirect |
| 42. #6099 | D4 | semidirect |
| 70. #413 | D13 | semidirect |
| 130. C13 | #1914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719535 | 2 |
| #11719524 | 2 |
| C13×#413 | 2 |
| C2×#88063 | 2 |
| #11718148 | 2 |
| #1914 | 13 |