Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 22. #5031 | C7 | direct (N × H) |
| 53. C3×C4×C7 | Q16 | semidirect |
| 92. C4×C7 | #216 | semidirect |
| 106. C3×C7 | #462 | semidirect |
| 124. C3×C4 | C7×Q16 | semidirect |
| 139. C7 | #5031 | direct (N × H) |
| 148. C4 | C7×#216 | semidirect |
| 151. C3 | C7×#462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C7×#216 | 2 |
| C7×#869 | 2 |
| C7×#810 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#462 | 3 |
| #5031 | 7 |