Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×#88059 | C2 | semidirect |
| 4. #11718762 | C2 | semidirect |
| 6. C13×#336 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 15. #88061 | C4 | semidirect |
| 16. #88061 | C4 | semidirect |
| 20. #88056 | C4 | semidirect |
| 21. #88056 | C4 | semidirect |
| 90. #336 | D13 | semidirect |
| 160. C13 | #1929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718774 | 2 |
| #11718771 | 2 |
| C2×#88059 | 2 |
| #11718762 | 2 |
| C2×#88045 | 2 |
| C13×#336 | 2 |
| #11718115 | 2 |
| #1929 | 13 |