Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. #10620507 | C2 | direct (N × H) |
| 10. C2×C7×Dic6 | C4 | semidirect |
| 31. C7×Dic6 | C2×C4 | semidirect |
| 78. C2×Dic6 | Dic7 | semidirect |
| 84. C2×C3×C7 | #103 | semidirect |
| 112. Dic6 | C2×Dic7 | semidirect |
| 114. C3×C7 | C2×#103 | semidirect |
| 126. C2×C7 | #810 | semidirect |
| 152. C7 | C2×#810 | semidirect |
| 153. C2×C3 | #6409 | semidirect |
| 166. C3 | C2×#6409 | semidirect |
| 167. C2 | #10620507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #10620507 | 2 |
| C2×#6409 | 3 |
| C2×#810 | 7 |