Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
225 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 55 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. #72246035 | C2 | semidirect |
| 2. ΓL(1,𝔽8)×C22⋊Dic7 | C2 | semidirect |
| 4. #13096072 | C3 | semidirect |
| 6. C22×C7×AGL(1,𝔽7) | C4 | semidirect |
| 11. C2×C7×ΓL(1,𝔽8)⋊C4 | C4 | semidirect |
| 13. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 14. C7×C22⋊Dic7 | C2×C3 | semidirect |
| 27. C22×C7×D7 | C3×C4 | semidirect |
| 32. C2×C7×Dic7 | C3×C4 | semidirect |
| 58. C22×AGL(1,𝔽7) | Dic7 | semidirect |
| 68. C2×ΓL(1,𝔽8)⋊C4 | Dic7 | semidirect |
| 69. C7×ΓL(1,𝔽8) | #99 | semidirect |
| 76. C22⋊Dic7 | AGL(1,𝔽7) | semidirect |
| 105. C22×D7 | C3×Dic7 | semidirect |
| 117. C2×Dic7 | C3×Dic7 | semidirect |
| 118. C72 | C3×#99 | semidirect |
| 166. ΓL(1,𝔽8) | #6408 | semidirect |
| 202. C7 | #6380⋊C3 | semidirect |
| 203. C7 | C3×#6408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72246035 | 2 |
| ΓL(1,𝔽8)×C22⋊Dic7 | 2 |
| C2×C7×(C22⋊D7)⋊C3 | 2 |
| #13096072 | 3 |
| C3×#6408 | 7 |
| #6380⋊C3 | 7 |