Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
684 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 203 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. C23×Dic21 | C2 | semidirect |
| 3. C2×C3×C7×C22⋊C4 | C2 | semidirect |
| 4. C2×#66631 | C2 | semidirect |
| 5. C2×C4⋊Dic21 | C2 | semidirect |
| 6. #10621369 | C2 | direct (N × H) |
| 16. C22×Dic21 | C22 | semidirect |
| 17. C3×C7×C22⋊C4 | C22 | semidirect |
| 18. #66631 | C22 | semidirect |
| 19. C4⋊Dic21 | C22 | semidirect |
| 22. C2×C7×C22⋊C4 | D3 | semidirect |
| 51. C7×C22⋊C4 | C2×D3 | semidirect |
| 56. C2×C3×C22⋊C4 | D7 | semidirect |
| 97. C3×C22⋊C4 | C2×D7 | semidirect |
| 101. C2×C3×C7 | #123 | semidirect |
| 110. C2×C22⋊C4 | D21 | semidirect |
| 138. C3×C7 | C2×#123 | semidirect |
| 150. C22⋊C4 | C2×D21 | semidirect |
| 152. C2×C7 | #886 | semidirect |
| 183. C7 | C2×#886 | semidirect |
| 185. C2×C3 | #6449 | semidirect |
| 201. C3 | C2×#6449 | semidirect |
| 204. C2 | #10621369 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4268 | 2 |
| C23×Dic21 | 2 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66631 | 2 |
| C2×C4⋊Dic21 | 2 |
| #10621369 | 2 |
| C2×#6449 | 3 |
| C2×#886 | 7 |