Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 7. C3×C7×M16 | C4 | semidirect |
| 14. C2×C7×C3⋊C8 | C4 | semidirect |
| 18. #4559 | C7 | direct (N × H) |
| 33. C7×M16 | Dic3 | semidirect |
| 64. C3×M16 | C4×C7 | semidirect |
| 71. C2×C3⋊C8 | C4×C7 | semidirect |
| 98. C3×C7 | #344 | semidirect |
| 103. M16 | C7×Dic3 | semidirect |
| 132. C7 | #4559 | direct (N × H) |
| 146. C3 | C7×#344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C7×#926 | 2 |
| C2×C7×#208 | 2 |
| C7×#344 | 3 |
| #4559 | 7 |