Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 13. C7×#216 | C4 | semidirect |
| 28. #4789 | C7 | direct (N × H) |
| 88. #216 | C4×C7 | semidirect |
| 128. C3×C7 | #441 | semidirect |
| 166. C7 | #4789 | direct (N × H) |
| 179. C3 | C7×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×Dic3 | 2 |
| C2×C7×#216 | 2 |
| C7×#887 | 2 |
| C3×C7×#103 | 2 |
| C7×#816 | 2 |
| C7×#815 | 2 |
| C7×#808 | 2 |
| C7×#441 | 3 |
| #4789 | 7 |