Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 82 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×C7×#204 | C2 | semidirect |
| 3. C7×#875 | C2 | semidirect |
| 4. C4×C7×D12 | C2 | semidirect |
| 5. C3×C7×C4⋊C8 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#816 | C2 | semidirect |
| 26. C7×C4⋊C8 | D3 | semidirect |
| 29. #4844 | C7 | direct (N × H) |
| 60. C2×#204 | C2×C7 | semidirect |
| 61. #875 | C2×C7 | semidirect |
| 62. C4×D12 | C2×C7 | semidirect |
| 63. C3×C4⋊C8 | C2×C7 | semidirect |
| 64. #821 | C2×C7 | semidirect |
| 65. #816 | C2×C7 | semidirect |
| 118. C4⋊C8 | D3×C7 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | #4844 | direct (N × H) |
| 217. C3 | C7×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×D24 | 2 |
| C2×C7×#204 | 2 |
| C7×#875 | 2 |
| C4×C7×D12 | 2 |
| C3×C7×C4⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#463 | 3 |
| #4844 | 7 |