Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 27. #5063 | C7 | direct (N × H) |
| 119. C3×C7 | #479 | semidirect |
| 154. C7 | #5063 | direct (N × H) |
| 167. C3 | C7×#479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#125 | 2 |
| C4×C7×Dic6 | 2 |
| C7×#810 | 2 |
| C7×#808 | 2 |
| C7×#807 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#479 | 3 |
| #5063 | 7 |