Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
164 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. D3×C7×Q16 | C2 | semidirect |
| 3. C3×C7×SD32 | C2 | semidirect |
| 4. C7×#829 | C2 | semidirect |
| 5. C7×#827 | C2 | semidirect |
| 6. C7×Dic24 | C2 | semidirect |
| 7. C7×#798 | C2 | semidirect |
| 25. C7×SD32 | D3 | semidirect |
| 27. #4915 | C7 | direct (N × H) |
| 50. D3×Q16 | C2×C7 | semidirect |
| 52. C3×SD32 | C2×C7 | semidirect |
| 53. #829 | C2×C7 | semidirect |
| 54. #827 | C2×C7 | semidirect |
| 55. Dic24 | C2×C7 | semidirect |
| 56. #798 | C2×C7 | semidirect |
| 95. SD32 | D3×C7 | semidirect |
| 115. C3×C7 | #510 | semidirect |
| 148. C7 | #4915 | direct (N × H) |
| 159. C3 | C7×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C7×Q16 | 2 |
| C7×#912 | 2 |
| C3×C7×SD32 | 2 |
| C7×#829 | 2 |
| C7×#827 | 2 |
| C7×Dic24 | 2 |
| C7×#798 | 2 |
| C7×#510 | 3 |
| #4915 | 7 |