Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
520 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 105 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. #72214657 | C2 | semidirect |
| 3. #13096150 | C3 | semidirect |
| 4. C23×#3861 | C4 | semidirect |
| 7. C2×C4×#3861 | C4 | semidirect |
| 10. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 20. C23×C72 | C3×C4 | semidirect |
| 23. C2×C4×C72 | C3×C4 | semidirect |
| 52. #3861 | #99 | semidirect |
| 76. C23×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 77. C23×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 82. C2×C4×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 83. C2×C4×C7 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 86. C72 | C3×#99 | semidirect |
| 136. C23 | #10596874 | semidirect |
| 140. C2×C4 | #10596874 | semidirect |
| 141. C7 | #6408⋊C3 | semidirect |
| 142. C7 | #6408⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72214657 | 2 |
| C2×D4×#3861 | 2 |
| #13096150 | 3 |
| #6408⋊C3 | 7 |