Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
238 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
| 11. C7×#208 | D3 | semidirect |
| 12. #63559 | C7 | direct (N × H) |
| 29. C3×#208 | C2×C7 | semidirect |
| 51. C32×C7 | #100 | semidirect |
| 59. #208 | D3×C7 | semidirect |
| 88. C3×C7 | #823 | semidirect |
| 108. C32 | C7×#100 | semidirect |
| 113. C7 | #63559 | direct (N × H) |
| 127. C3 | C7×#823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C4⋊(C3⋊D3) | 2 |
| C3×C7×#208 | 2 |
| C7×#823 | 3 |
| #63559 | 7 |