Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×C7×Dic6 | C2 | semidirect |
| 3. C2×C3×C4×Dic7 | C2 | semidirect |
| 4. C2×#66575 | C2 | semidirect |
| 5. #10620937 | C2 | direct (N × H) |
| 13. C2×C7×Dic6 | C22 | semidirect |
| 15. C3×C4×Dic7 | C22 | semidirect |
| 16. #66575 | C22 | semidirect |
| 21. C2×C4×Dic7 | D3 | semidirect |
| 44. C4×Dic7 | C2×D3 | semidirect |
| 46. C22×Dic6 | D7 | semidirect |
| 79. C2×Dic6 | C2×D7 | semidirect |
| 82. C2×C3×C7 | #124 | semidirect |
| 112. C3×C7 | C2×#124 | semidirect |
| 123. C2×C7 | #875 | semidirect |
| 148. C7 | C2×#875 | semidirect |
| 149. C2×C3 | #6510 | semidirect |
| 162. C3 | C2×#6510 | semidirect |
| 164. C2 | #10620937 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×C7×Dic6 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×#66575 | 2 |
| #10620937 | 2 |
| C2×#6510 | 3 |
| C2×#875 | 7 |