Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 37 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×#100 | C2 | semidirect |
| 3. #10620673 | C2 | semidirect |
| 5. C23×D21 | C4 | semidirect |
| 10. #66636 | C4 | semidirect |
| 13. C7×#100 | D3 | semidirect |
| 35. C3×#100 | D7 | semidirect |
| 75. #100 | D21 | semidirect |
| 101. C3×C7 | AΣL(1,𝔽16) | semidirect |
| 138. C7 | #4475 | semidirect |
| 157. C3 | #89270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621420 | 2 |
| C3×C7×#100 | 2 |
| #10620673 | 2 |
| #89270 | 3 |
| #4475 | 7 |