Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 3. C3×#6392 | C2 | semidirect |
| 4. C3×#6391 | C2 | semidirect |
| 5. #89878 | C3 | direct (N × H) |
| 7. C2×C3×C7×C8 | C4 | semidirect |
| 15. #6392 | C2×C3 | semidirect |
| 16. #6391 | C2×C3 | semidirect |
| 27. C2×C7×C8 | C3×C4 | semidirect |
| 54. C2×C3×C8 | Dic7 | semidirect |
| 82. C3×C7 | #427 | semidirect |
| 84. C2×C8 | C3×Dic7 | semidirect |
| 108. C7 | C3×#427 | semidirect |
| 119. C3 | #89878 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×C8 | 2 |
| C3×#6489 | 2 |
| C3×#6392 | 2 |
| C3×#6391 | 2 |
| #89878 | 3 |
| C3×#427 | 7 |