Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 324 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. C3×C7×#103 | C2 | semidirect |
| 5. C7×#835 | C2 | semidirect |
| 6. C7×#816 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 11. D3×C7×Q8 | C4 | semidirect |
| 29. C7×#103 | D3 | direct (N × H) |
| 30. D3×#103 | C7 | direct (N × H) |
| 33. C3×C7×Q8 | C2×C4 | semidirect |
| 46. C7×Dic6 | C2×C4 | semidirect |
| 66. C3×#103 | C2×C7 | semidirect |
| 67. #835 | C2×C7 | semidirect |
| 68. #816 | C2×C7 | semidirect |
| 69. #810 | C2×C7 | semidirect |
| 87. C7×Q8 | C4×D3 | semidirect |
| 102. D3×Q8 | C4×C7 | semidirect |
| 117. D3×C7 | #103 | direct (N × H) |
| 124. #103 | D3×C7 | direct (N × H) |
| 138. C3×Q8 | C2×C4×C7 | semidirect |
| 151. Dic6 | C2×C4×C7 | semidirect |
| 154. C3×C7 | C2×#103 | semidirect |
| 189. Q8 | C4×D3×C7 | semidirect |
| 202. C7 | D3×#103 | direct (N × H) |
| 206. D3 | C7×#103 | direct (N × H) |
| 218. C3 | C2×C7×#103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×D3×C7×C8 | 2 |
| D3×C7×C4⋊C4 | 2 |
| C3×C7×#103 | 2 |
| C7×#835 | 2 |
| C7×#816 | 2 |
| C7×#810 | 2 |
| C2×C7×#103 | 3 |
| D3×#103 | 7 |