Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 102 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. C4×C7×Dic6 | C2 | semidirect |
| 4. C3×C7×#97 | C2 | semidirect |
| 6. C7×#818 | C2 | semidirect |
| 7. C7×#816 | C2 | semidirect |
| 20. C7×#204 | C4 | semidirect |
| 27. C7×#97 | D3 | semidirect |
| 28. #4710 | C7 | direct (N × H) |
| 40. C7×Dic6 | C2×C4 | semidirect |
| 42. C3×C7×C8 | C2×C4 | semidirect |
| 57. C4×Dic6 | C2×C7 | semidirect |
| 58. C3×#97 | C2×C7 | semidirect |
| 60. #818 | C2×C7 | semidirect |
| 61. #816 | C2×C7 | semidirect |
| 87. C7×C8 | C4×D3 | semidirect |
| 99. #204 | C4×C7 | semidirect |
| 110. #97 | D3×C7 | semidirect |
| 133. Dic6 | C2×C4×C7 | semidirect |
| 135. C3×C8 | C2×C4×C7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 177. C8 | C4×D3×C7 | semidirect |
| 178. C7 | #4710 | direct (N × H) |
| 194. C3 | C7×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#204 | 2 |
| C4×C7×D12 | 2 |
| C4×C7×Dic6 | 2 |
| C3×C7×#97 | 2 |
| C7×#821 | 2 |
| C7×#818 | 2 |
| C7×#816 | 2 |
| C7×#440 | 3 |
| #4710 | 7 |