Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 3. C2×C4×Dic26 | C2 | semidirect |
| 5. C4×#6105 | C2 | direct (N × H) |
| 6. C2×#88050 | C2 | semidirect |
| 7. C2×#88048 | C2 | semidirect |
| 8. C2×C4×#1055 | C2 | semidirect |
| 17. C2×#6105 | C4 | direct (N × H) |
| 25. C4×Dic26 | C22 | semidirect |
| 27. #88050 | C22 | semidirect |
| 28. #88048 | C22 | semidirect |
| 29. C4×#1055 | C22 | semidirect |
| 45. C2×Dic26 | C2×C4 | semidirect |
| 52. #6105 | C2×C4 | direct (N × H) |
| 58. C2×#1055 | C2×C4 | semidirect |
| 74. C2×C4×C13 | SD16 | semidirect |
| 87. Dic26 | C22×C4 | semidirect |
| 89. #1055 | C22×C4 | semidirect |
| 109. C4×C13 | C2×SD16 | semidirect |
| 136. C2×C13 | C4×SD16 | semidirect |
| 171. C13 | C2×C4×SD16 | semidirect |
| 191. C2×C4 | #6105 | direct (N × H) |
| 213. C4 | C2×#6105 | direct (N × H) |
| 217. C2 | C4×#6105 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C22×#6105 | 2 |
| C2×C4×Dic26 | 2 |
| C2×#88072 | 2 |
| C4×#6105 | 2 |
| C2×#88050 | 2 |
| C2×#88048 | 2 |
| C2×C4×#1055 | 2 |
| C2×C4×SD16 | 13 |