Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 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. C3×C7×#208 | C2 | semidirect |
| 4. C7×#833 | C3 | direct (N × H) |
| 13. C7×#208 | C2×C3 | semidirect |
| 14. C3×#833 | C7 | direct (N × H) |
| 33. C3×#208 | C2×C7 | semidirect |
| 40. #833 | C3×C7 | direct (N × H) |
| 59. C32×C7 | #100 | semidirect |
| 68. #208 | C2×C3×C7 | semidirect |
| 102. C3×C7 | #833 | direct (N × H) |
| 103. C3×C7 | C3×#100 | semidirect |
| 126. C32 | C7×#100 | semidirect |
| 131. C7 | C3×#833 | direct (N × H) |
| 148. C3 | C7×#833 | direct (N × H) |
| 149. C3 | C3×C7×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C7×D4 | 2 |
| C3×C7×#208 | 2 |
| C3×C7×#100 | 3 |
| C7×#833 | 3 |
| C3×#833 | 7 |