Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 3. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 4. C3×C7×#95 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 13. C2×C4×D3×C7 | C4 | semidirect |
| 20. C7×#95 | D3 | semidirect |
| 21. #4667 | C7 | direct (N × H) |
| 50. C2×Dic3⋊C4 | C2×C7 | semidirect |
| 51. C3×#95 | C2×C7 | semidirect |
| 52. C3⋊#95 | C2×C7 | semidirect |
| 62. C2×D3×C7 | C4⋊C4 | semidirect |
| 66. C7×Dic3 | C22⋊C4 | semidirect |
| 91. C2×C4×D3 | C4×C7 | semidirect |
| 104. #95 | D3×C7 | semidirect |
| 136. C3×C7 | #380 | semidirect |
| 161. C2×D3 | C7×C4⋊C4 | semidirect |
| 165. Dic3 | C7×C22⋊C4 | semidirect |
| 183. C7 | #4667 | direct (N × H) |
| 204. C3 | C7×#380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3×C7 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C3×C7×#95 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#380 | 3 |
| #4667 | 7 |