Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1012 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 190 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×C3×C7×C22⋊C4 | C2 | semidirect |
| 3. C2×C7×#217 | C2 | semidirect |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 10. C23×D3×C7 | C4 | semidirect |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 13. C22×C7×Dic3 | C22 | semidirect |
| 20. C2×C7×C22⋊C4 | D3 | semidirect |
| 21. #4955 | C7 | direct (N × H) |
| 47. C22×C4×C7 | C2×D3 | semidirect |
| 52. C2×C3×C22⋊C4 | C2×C7 | semidirect |
| 53. C2×#217 | C2×C7 | semidirect |
| 54. C2×(C2×D3)⋊C4 | C2×C7 | semidirect |
| 58. C22×C3×C7 | C22⋊C4 | semidirect |
| 68. C2×D3×C7 | C22⋊C4 | semidirect |
| 94. C23×D3 | C4×C7 | semidirect |
| 96. C22×C3×C4 | C22×C7 | semidirect |
| 97. C22×Dic3 | C22×C7 | semidirect |
| 110. C2×C22⋊C4 | D3×C7 | semidirect |
| 120. C22×C7 | (C2×D3)⋊C4 | semidirect |
| 145. C3×C7 | #379 | semidirect |
| 153. C22×C4 | C2×D3×C7 | semidirect |
| 166. C22×C3 | C7×C22⋊C4 | semidirect |
| 176. C2×D3 | C7×C22⋊C4 | semidirect |
| 197. C7 | #4955 | direct (N × H) |
| 213. C22 | C7×(C2×D3)⋊C4 | semidirect |
| 220. C3 | C7×#379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D3×C7 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×C7×#217 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C7×#379 | 3 |
| #4955 | 7 |