Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. C13×#537 | C2 | semidirect |
| 2. #11719538 | C2 | semidirect |
| 3. C2×#88204 | C2 | semidirect |
| 4. C2×#88202 | C2 | semidirect |
| 5. #11718893 | C2 | semidirect |
| 6. #11718712 | C2 | semidirect |
| 7. #11718710 | C2 | semidirect |
| 8. #11718703 | C2 | semidirect |
| 9. #11718699 | C2 | semidirect |
| 10. #11718627 | C2 | semidirect |
| 11. C2×#88047 | C2 | semidirect |
| 83. C2×#1055 | D4 | semidirect |
| 128. #537 | D13 | semidirect |
| 239. C13 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#537 | 2 |
| #11719538 | 2 |
| C2×#88204 | 2 |
| C2×#88202 | 2 |
| #11718893 | 2 |
| #11718712 | 2 |
| #11718710 | 2 |
| #11718703 | 2 |
| #11718699 | 2 |
| #11718627 | 2 |
| C2×#88047 | 2 |
| #3061 | 13 |