Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 15. C7×#216 | C4 | direct (N × H) |
| 28. C4×#216 | C7 | direct (N × H) |
| 65. C3×C4×C7 | Q16 | semidirect |
| 90. #216 | C4×C7 | direct (N × H) |
| 112. C4×C7 | #216 | direct (N × H) |
| 128. C3×C7 | C4×Q16 | semidirect |
| 148. C3×C4 | C7×Q16 | semidirect |
| 166. C7 | C4×#216 | direct (N × H) |
| 176. C4 | C7×#216 | direct (N × H) |
| 179. C3 | C4×C7×Q16 | 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 |
| C4×C7×Dic6 | 2 |
| C7×#835 | 2 |
| C7×#810 | 2 |
| C7×#807 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C4×C7×Q16 | 3 |
| C4×#216 | 7 |