Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
308 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 8. C3×C42×C7 | C4 | semidirect |
| 13. #4936 | C7 | direct (N × H) |
| 26. C42×C7 | Dic3 | semidirect |
| 49. C3×C42 | C4×C7 | semidirect |
| 73. C3×C7 | #382 | semidirect |
| 78. C42 | C7×Dic3 | semidirect |
| 98. C7 | #4936 | direct (N × H) |
| 110. C3 | C7×#382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#382 | 3 |
| #4936 | 7 |