Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
211 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 66 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. C7×#1136⋊C3 | C2 | semidirect |
| 3. C7×#6407 | C3 | semidirect |
| 9. C7×#1136 | C2×C3 | semidirect |
| 11. #6407⋊C3 | C7 | direct (N × H) |
| 23. #1136⋊C3 | C2×C7 | semidirect |
| 28. #6407 | C3×C7 | semidirect |
| 41. C7×ΓL(1,𝔽8) | #100 | semidirect |
| 46. #1136 | C2×C3×C7 | semidirect |
| 71. C72 | C3×#100 | semidirect |
| 100. ΓL(1,𝔽8) | C7×#100 | semidirect |
| 123. C7 | #6407⋊C3 | direct (N × H) |
| 124. C7 | C3×C7×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1136⋊C3 | 2 |
| C2×C7×D4×ΓL(1,𝔽8) | 2 |
| C7×#6407 | 3 |
| C3×C7×#100 | 7 |
| #6407⋊C3 | 7 |