Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 4. C4×C22⋊Dic13 | C2 | semidirect |
| 5. #11718642 | C2 | semidirect |
| 6. C4⋊C4×Dic13 | C2 | semidirect |
| 7. #11718612 | C2 | semidirect |
| 8. #11718612 | C2 | semidirect |
| 9. C22⋊C4×Dic13 | C2 | semidirect |
| 13. C13×#123 | C4 | semidirect |
| 39. C22×C4×C13 | C2×C4 | semidirect |
| 49. C13×C4⋊C4 | C2×C4 | semidirect |
| 51. C13×C22⋊C4 | C2×C4 | semidirect |
| 132. #123 | Dic13 | semidirect |
| 171. C22×C4 | C2×Dic13 | semidirect |
| 177. C4⋊C4 | C2×Dic13 | semidirect |
| 183. C22⋊C4 | C2×Dic13 | semidirect |
| 188. C13 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#123 | 2 |
| #11718882 | 2 |
| #11718881 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718642 | 2 |
| C4⋊C4×Dic13 | 2 |
| #11718612 | 2 |
| C22⋊C4×Dic13 | 2 |
| #2374 | 13 |