Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C7×#816 | C2 | semidirect |
| 10. C2×C7×Dic6 | C4 | semidirect |
| 21. #5120 | C7 | direct (N × H) |
| 48. #816 | C2×C7 | semidirect |
| 74. C2×Dic6 | C4×C7 | semidirect |
| 108. C3×C7 | #419 | semidirect |
| 143. C7 | #5120 | direct (N × H) |
| 155. C3 | C7×#419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C2×C3×C7×M16 | 2 |
| C7×#926 | 2 |
| C7×#816 | 2 |
| C7×#419 | 3 |
| #5120 | 7 |