Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 2. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 3. C3×C7×C22⋊C8 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 5. C7×#817 | C2 | semidirect |
| 20. C7×C22⋊C8 | D3 | semidirect |
| 21. #4735 | C7 | direct (N × H) |
| 43. C2×C4⋊Dic3 | C2×C7 | semidirect |
| 44. C3×C22⋊C8 | C2×C7 | semidirect |
| 45. #821 | C2×C7 | semidirect |
| 46. #817 | C2×C7 | semidirect |
| 88. C22⋊C8 | D3×C7 | semidirect |
| 111. C3×C7 | #481 | semidirect |
| 148. C7 | #4735 | direct (N × H) |
| 165. C3 | C7×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#930 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#817 | 2 |
| C7×#481 | 3 |
| #4735 | 7 |