Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
274 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 87 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. C2×#88058 | C2 | semidirect |
| 4. C2×#88057 | C2 | semidirect |
| 6. #11718597 | C2 | semidirect |
| 7. C13×#336 | C2 | semidirect |
| 82. #336 | D13 | semidirect |
| 147. C13 | #2092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88061 | 2 |
| C2×#88058 | 2 |
| C2×#88057 | 2 |
| #11718600 | 2 |
| #11718597 | 2 |
| C13×#336 | 2 |
| #2092 | 13 |