Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #72245172 | C2 | semidirect |
| 3. #13096152 | C3 | semidirect |
| 9. #11716066 | C2×C3 | semidirect |
| 42. C7×ΓL(1,𝔽8) | #100 | semidirect |
| 73. C72 | C3×#100 | semidirect |
| 100. ΓL(1,𝔽8) | #6407 | semidirect |
| 121. C7 | #6407⋊C3 | semidirect |
| 122. C7 | C3×#6407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72245172 | 2 |
| C2×C7×D4×ΓL(1,𝔽8) | 2 |
| #13096152 | 3 |
| C3×#6407 | 7 |
| #6407⋊C3 | 7 |