Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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×#88123 | C2 | semidirect |
| 4. C13×#423 | C2 | semidirect |
| 5. #11718781 | C2 | semidirect |
| 6. #11718510 | C2 | semidirect |
| 7. #11718502 | C2 | semidirect |
| 86. #423 | D13 | semidirect |
| 95. C4×C13 | #137 | semidirect |
| 153. C13 | #3039 | semidirect |
| 188. C4 | #88163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| C4×#6127 | 2 |
| C2×#88123 | 2 |
| C13×#423 | 2 |
| #11718781 | 2 |
| #11718510 | 2 |
| #11718502 | 2 |
| #3039 | 13 |