Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
420 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 107 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×C22⋊C4 | C2 | semidirect |
| 3. C2×#66636 | C2 | semidirect |
| 4. #10620645 | C2 | direct (N × H) |
| 7. C23×D21 | C4 | semidirect |
| 13. C2×#4268 | C4 | semidirect |
| 16. C22×Dic21 | C4 | semidirect |
| 18. C3×C7×C22⋊C4 | C22 | semidirect |
| 20. #66636 | C22 | semidirect |
| 22. C2×C7×C22⋊C4 | D3 | semidirect |
| 37. C22×D21 | C2×C4 | semidirect |
| 48. C2×Dic21 | C2×C4 | semidirect |
| 61. C7×C22⋊C4 | C2×D3 | semidirect |
| 65. C2×C3×C22⋊C4 | D7 | semidirect |
| 125. C3×C22⋊C4 | C2×D7 | semidirect |
| 134. C2×C3×C7 | #99 | semidirect |
| 139. C2×C22⋊C4 | D21 | semidirect |
| 185. C3×C7 | C2×#99 | semidirect |
| 200. C22⋊C4 | C2×D21 | semidirect |
| 207. C2×C7 | #806 | semidirect |
| 254. C7 | C2×#806 | semidirect |
| 261. C2×C3 | #6380 | semidirect |
| 285. C3 | C2×#6380 | semidirect |
| 293. C2 | #10620645 | 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 |
| C2×C3×C7×C22⋊C4 | 2 |
| C2×#66636 | 2 |
| #10620645 | 2 |
| C2×#6380 | 3 |
| C2×#806 | 7 |