Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #11719530 | C2 | semidirect |
| 3. C2×#88205 | C2 | semidirect |
| 4. C2×#88202 | C2 | semidirect |
| 5. #11718894 | C2 | semidirect |
| 6. #11718713 | C2 | semidirect |
| 7. #11718712 | C2 | semidirect |
| 8. #11718703 | C2 | semidirect |
| 9. #11718702 | C2 | semidirect |
| 10. C2×#88050 | C2 | semidirect |
| 11. #11718625 | C2 | semidirect |
| 79. #6099 | D4 | semidirect |
| 228. C13 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#537 | 2 |
| #11719530 | 2 |
| C2×#88205 | 2 |
| C2×#88202 | 2 |
| #11718894 | 2 |
| #11718713 | 2 |
| #11718712 | 2 |
| #11718703 | 2 |
| #11718702 | 2 |
| C2×#88050 | 2 |
| #11718625 | 2 |
| #3063 | 13 |