Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#88205 | C2 | semidirect |
| 3. C2×#88163 | C2 | semidirect |
| 4. C2×C13×#104 | C2 | semidirect |
| 5. #11718590 | C2 | semidirect |
| 6. C2×#88045 | C2 | semidirect |
| 7. #11718146 | C2 | semidirect |
| 57. C2×Dic26 | D4 | semidirect |
| 59. C13×M16 | D4 | semidirect |
| 71. #6099 | D4 | semidirect |
| 122. C2×#104 | D13 | semidirect |
| 209. M16 | C22⋊D13 | semidirect |
| 219. C13 | #2007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719538 | 2 |
| C2×#88205 | 2 |
| C2×#88163 | 2 |
| C2×C13×#104 | 2 |
| #11718590 | 2 |
| C2×#88045 | 2 |
| #11718146 | 2 |
| #2007 | 13 |