Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 185 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. #11719227 | C2 | semidirect |
| 3. C13×#427 | C2 | semidirect |
| 4. C2×C8×Dic13 | C2 | semidirect |
| 5. #11718663 | C2 | semidirect |
| 6. #11718534 | C2 | semidirect |
| 7. #11718533 | C2 | semidirect |
| 8. #11718513 | C2 | semidirect |
| 15. #88158 | C4 | semidirect |
| 33. #6127 | C2×C4 | semidirect |
| 38. C2×C8×C13 | C2×C4 | semidirect |
| 52. Dic52 | C2×C4 | semidirect |
| 53. D104 | C2×C4 | semidirect |
| 54. #6095 | C2×C4 | semidirect |
| 82. #427 | D13 | semidirect |
| 96. Dic13 | #135 | semidirect |
| 135. C2×C8 | C4×D13 | semidirect |
| 147. C13 | C4×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88158 | 2 |
| #11719227 | 2 |
| C13×#427 | 2 |
| C2×C8×Dic13 | 2 |
| #11718663 | 2 |
| #11718534 | 2 |
| #11718533 | 2 |
| #11718513 | 2 |
| C4×#135 | 13 |