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 |
|---|---|---|
| 2. C2×C3×C7×M16 | C2 | semidirect |
| 3. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 4. C7×#821 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 11. C7×#235 | C4 | semidirect |
| 20. C2×C7×M16 | D3 | semidirect |
| 24. #5133 | C7 | direct (N × H) |
| 36. C7×D12 | C2×C4 | semidirect |
| 39. C7×Dic6 | C2×C4 | semidirect |
| 54. C2×C3×M16 | C2×C7 | semidirect |
| 55. C2×C4⋊Dic3 | C2×C7 | semidirect |
| 56. #821 | C2×C7 | semidirect |
| 57. #816 | C2×C7 | semidirect |
| 91. #235 | C4×C7 | semidirect |
| 105. C2×M16 | D3×C7 | semidirect |
| 132. D12 | C2×C4×C7 | semidirect |
| 135. Dic6 | C2×C4×C7 | semidirect |
| 137. C3×C7 | #417 | semidirect |
| 183. C7 | #5133 | direct (N × H) |
| 201. C3 | C7×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×C3×C7×M16 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#417 | 3 |
| #5133 | 7 |