Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
191 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 46 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. C4×#10596875 | C2 | semidirect |
| 3. #72245059 | C2 | semidirect |
| 4. #13096060 | C3 | semidirect |
| 8. C4⋊#64422 | C4 | semidirect |
| 10. #11924208 | C4 | semidirect |
| 13. C4×C7⋊Dic7 | C2×C3 | semidirect |
| 14. C7×#1136 | C2×C3 | semidirect |
| 26. C7×D28 | C3×C4 | semidirect |
| 28. C7×Dic14 | C3×C4 | semidirect |
| 61. #3862 | #104 | semidirect |
| 68. #1136 | AGL(1,𝔽7) | semidirect |
| 97. D28 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 99. Dic14 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 102. C72 | C3×#104 | semidirect |
| 165. C7 | #6399⋊C3 | semidirect |
| 166. C7 | #6411⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#10596875 | 2 |
| #72245079 | 2 |
| #72245059 | 2 |
| #13096060 | 3 |
| #6411⋊C3 | 7 |
| #6399⋊C3 | 7 |