Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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 |
|---|---|---|
| 1. C22×C3×C7×Q8 | C2 | semidirect |
| 3. C7×C3⋊#95 | C2 | semidirect |
| 10. C22×C7×Q8 | D3 | semidirect |
| 13. #5231 | C7 | direct (N × H) |
| 17. C22×D3×C7 | Q8 | semidirect |
| 28. C22×C3×Q8 | C2×C7 | semidirect |
| 30. C3⋊#95 | C2×C7 | semidirect |
| 58. C22×Q8 | D3×C7 | semidirect |
| 72. C22×D3 | C7×Q8 | semidirect |
| 78. C3×C7 | #393 | semidirect |
| 105. C7 | #5231 | direct (N × H) |
| 118. C3 | C7×#393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×Q8 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#393 | 3 |
| #5231 | 7 |