Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 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. C7×#924 | C2 | semidirect |
| 3. C2×C7×Dic12 | C2 | semidirect |
| 4. C2×C7×#204 | C2 | semidirect |
| 5. C3×C7×C22⋊C8 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#816 | C2 | semidirect |
| 30. C7×C22⋊C8 | D3 | semidirect |
| 31. #4733 | C7 | direct (N × H) |
| 67. #924 | C2×C7 | semidirect |
| 68. C2×Dic12 | C2×C7 | semidirect |
| 69. C2×#204 | C2×C7 | semidirect |
| 70. C3×C22⋊C8 | C2×C7 | semidirect |
| 71. #821 | C2×C7 | semidirect |
| 72. #816 | C2×C7 | semidirect |
| 132. C22⋊C8 | D3×C7 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | #4733 | direct (N × H) |
| 237. C3 | C7×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C7×#924 | 2 |
| C2×C7×Dic12 | 2 |
| C2×C7×#204 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#821 | 2 |
| C7×#816 | 2 |
| C7×#452 | 3 |
| #4733 | 7 |