Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 2. C3×C7×#99 | C2 | semidirect |
| 3. C7×#833 | C2 | semidirect |
| 5. C23×D3×C7 | C4 | semidirect |
| 9. C7×#217 | C4 | semidirect |
| 14. C7×#99 | D3 | semidirect |
| 15. #4471 | C7 | direct (N × H) |
| 35. C3×#99 | C2×C7 | semidirect |
| 36. #833 | C2×C7 | semidirect |
| 62. C23×D3 | C4×C7 | semidirect |
| 66. #217 | C4×C7 | semidirect |
| 76. #99 | D3×C7 | semidirect |
| 101. C3×C7 | AΣL(1,𝔽16) | semidirect |
| 138. C7 | #4471 | direct (N × H) |
| 157. C3 | C7×AΣL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#937 | 2 |
| C3×C7×#99 | 2 |
| C7×#833 | 2 |
| C7×AΣL(1,𝔽16) | 3 |
| #4471 | 7 |