Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×#88069 | C2 | semidirect |
| 5. C13×#358 | C2 | semidirect |
| 6. #11718095 | C2 | semidirect |
| 7. #11718082 | C2 | semidirect |
| 63. #358 | D13 | semidirect |
| 111. C13 | #2219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718849 | 2 |
| C2×#88069 | 2 |
| C2×#88038 | 2 |
| #11718548 | 2 |
| C13×#358 | 2 |
| #11718095 | 2 |
| #11718082 | 2 |
| #2219 | 13 |