Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
940 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 940 conjugacy classes of subgroups — too many to draw. Only its 235 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. C22×#10596874 | C2 | semidirect |
| 2. #72228595 | C2 | semidirect |
| 3. #72214657 | C2 | semidirect |
| 4. C4×#10596874 | C2 | semidirect |
| 6. D4×C7⋊Dic7 | C3 | semidirect |
| 8. D4×#3861 | C4 | semidirect |
| 15. C22×C7⋊Dic7 | C2×C3 | semidirect |
| 16. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 17. C4⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 18. C4×C7⋊Dic7 | C2×C3 | semidirect |
| 23. C22×#3861 | C2×C4 | semidirect |
| 25. C4×#3861 | C2×C4 | semidirect |
| 28. #10596874 | D4 | direct (N × H) |
| 30. C72×D4 | C3×C4 | semidirect |
| 54. C22×C72 | C2×C3×C4 | semidirect |
| 56. C4×C72 | C2×C3×C4 | semidirect |
| 59. C7⋊Dic7 | C3×D4 | semidirect |
| 74. #3861 | C4×D4 | semidirect |
| 108. C7×D4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 109. C7×D4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 120. C72 | C3×C4×D4 | semidirect |
| 139. C22×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 140. C22×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 143. C4×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 144. C4×C7 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 182. D4 | #10596874 | direct (N × H) |
| 188. C7 | D4×ΓL(1,𝔽8)⋊C4 | semidirect |
| 189. C7 | D4×ΓL(1,𝔽8)⋊C4 | semidirect |
| 196. C22 | C2×#10596874 | semidirect |
| 201. C4 | C2×#10596874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596874 | 2 |
| #72228595 | 2 |
| #72214657 | 2 |
| C4×#10596874 | 2 |
| C2×D4×#3861 | 2 |
| D4×C7⋊Dic7 | 3 |
| D4×ΓL(1,𝔽8)⋊C4 | 7 |