Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C7×C4⋊Q8 | C2 | semidirect |
| 3. C7×#809 | C2 | semidirect |
| 4. C4×C7×C3⋊C8 | C2 | semidirect |
| 14. C7×C4⋊Q8 | D3 | semidirect |
| 18. #5088 | C7 | direct (N × H) |
| 37. C3×C4⋊Q8 | C2×C7 | semidirect |
| 39. #809 | C2×C7 | semidirect |
| 40. C4×C3⋊C8 | C2×C7 | semidirect |
| 72. C4⋊Q8 | D3×C7 | semidirect |
| 94. C3×C7 | #486 | semidirect |
| 125. C7 | #5088 | direct (N × H) |
| 138. C3 | C7×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C7×#874 | 2 |
| C7×#809 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#486 | 3 |
| #5088 | 7 |