Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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. C13×#419 | C2 | semidirect |
| 4. C2×#88076 | C2 | semidirect |
| 6. #11718152 | C2 | semidirect |
| 7. #11718125 | C2 | semidirect |
| 12. C2×#6107 | C4 | semidirect |
| 15. C2×#6106 | C4 | semidirect |
| 93. #419 | D13 | semidirect |
| 167. C13 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88196 | 2 |
| #11719450 | 2 |
| C13×#419 | 2 |
| C2×#88076 | 2 |
| #11718666 | 2 |
| #11718152 | 2 |
| #11718125 | 2 |
| #1902 | 13 |