Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 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. #11719205 | C2 | semidirect |
| 5. #11718767 | C2 | semidirect |
| 6. #11718763 | C2 | semidirect |
| 7. #11718625 | C2 | semidirect |
| 8. #11718427 | C2 | semidirect |
| 9. #11718424 | C2 | semidirect |
| 10. #11718422 | C2 | semidirect |
| 11. #11718420 | C2 | semidirect |
| 26. #88144 | C22 | semidirect |
| 28. #88142 | C22 | semidirect |
| 33. #88058 | C22 | semidirect |
| 34. #88058 | C22 | semidirect |
| 35. #88057 | C22 | semidirect |
| 36. #88057 | C22 | semidirect |
| 37. #88054 | C22 | semidirect |
| 38. #88054 | C22 | semidirect |
| 39. #88048 | C22 | semidirect |
| 40. #88047 | C22 | semidirect |
| 44. C2×D4×C13 | Q8 | semidirect |
| 169. C2×D4 | Dic26 | semidirect |
| 199. C13 | #3081 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719503 | 2 |
| #11719205 | 2 |
| C2×C13×#102 | 2 |
| #11718876 | 2 |
| #11718767 | 2 |
| #11718763 | 2 |
| #11718625 | 2 |
| #11718427 | 2 |
| #11718424 | 2 |
| #11718422 | 2 |
| #11718420 | 2 |
| #3081 | 13 |