Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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. C13×#419 | C2 | semidirect |
| 3. C2×#88076 | C2 | semidirect |
| 5. C2×#88062 | C2 | semidirect |
| 7. #11718658 | C2 | semidirect |
| 15. C2×#6106 | C4 | semidirect |
| 90. #419 | D13 | semidirect |
| 165. C13 | #1977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6106 | 2 |
| C13×#419 | 2 |
| C2×#88076 | 2 |
| C2×#88063 | 2 |
| C2×#88062 | 2 |
| #11718662 | 2 |
| #11718658 | 2 |
| #1977 | 13 |