Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
160 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 58 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. C2×C7×Dic6 | C4 | semidirect |
| 10. C7×C4⋊Dic3 | C4 | semidirect |
| 15. #4467 | C7 | direct (N × H) |
| 61. C2×Dic6 | C4×C7 | semidirect |
| 64. C4⋊Dic3 | C4×C7 | semidirect |
| 95. C3×C7 | #328 | semidirect |
| 129. C7 | #4467 | direct (N × H) |
| 145. C3 | C7×#328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#924 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#328 | 3 |
| #4467 | 7 |