Finite Group DatabasebetaFinite Group DatabasebetaOrder 4704.
520 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 2. C22⋊C4×#3861 | C2 | semidirect |
| 4. #13096124 | C3 | semidirect |
| 6. C22×#64424 | C4 | semidirect |
| 11. C2×#10596874 | C4 | semidirect |
| 13. C72×C22⋊C4 | C2×C3 | semidirect |
| 14. C22⋊(C7⋊Dic7) | C2×C3 | semidirect |
| 27. C22×C7⋊D7 | C3×C4 | semidirect |
| 32. C2×C7⋊Dic7 | C3×C4 | semidirect |
| 69. #3861 | #99 | semidirect |
| 72. C7×C22⋊C4 | AGL(1,𝔽7) | semidirect |
| 73. C7×C22⋊C4 | AGL(1,𝔽7) | semidirect |
| 114. C72 | C3×#99 | semidirect |
| 158. C22⋊C4 | #64424 | semidirect |
| 185. C7 | #6380⋊C3 | semidirect |
| 186. C7 | #6380⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72214657 | 2 |
| C22⋊C4×#3861 | 2 |
| C2×#11924217 | 2 |
| #13096124 | 3 |
| #6380⋊C3 | 7 |