Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×C13×2−1+4 | C2 | semidirect |
| 2. #11719535 | C2 | semidirect |
| 3. C2×#88203 | C2 | semidirect |
| 4. C22×#6106 | C2 | semidirect |
| 5. #11718899 | C2 | semidirect |
| 6. #11718895 | C2 | semidirect |
| 7. #11718894 | C2 | semidirect |
| 8. #11718888 | C2 | semidirect |
| 9. #11718886 | C2 | semidirect |
| 16. C2×C13×#41 | C22 | semidirect |
| 19. C22×Q8×C13 | C22 | semidirect |
| 33. #88075 | C22 | semidirect |
| 34. #88075 | C22 | semidirect |
| 35. #88072 | C22 | semidirect |
| 36. C22⋊#1055 | C22 | semidirect |
| 45. C13×#41 | D4 | semidirect |
| 53. C2×Q8×C13 | D4 | semidirect |
| 123. C2×2−1+4 | D13 | semidirect |
| 155. C2×#41 | C2×D13 | semidirect |
| 158. C22×Q8 | C2×D13 | semidirect |
| 190. #41 | C22⋊D13 | semidirect |
| 198. C2×Q8 | C22⋊D13 | semidirect |
| 228. C13 | #3010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×2−1+4 | 2 |
| #11719535 | 2 |
| C2×#88203 | 2 |
| C22×#6106 | 2 |
| #11718899 | 2 |
| #11718895 | 2 |
| #11718894 | 2 |
| #11718888 | 2 |
| #11718886 | 2 |
| #3010 | 13 |