Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
140 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 30 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 |
|---|---|---|
| 16. #5416 | C7 | direct (N × H) |
| 38. C7×A4 | Q16 | semidirect |
| 72. C22×C7 | #216 | semidirect |
| 101. A4 | C7×Q16 | semidirect |
| 120. C7 | #5416 | direct (N × H) |
| 124. C22 | C7×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×A4 | 2 |
| C7×A4⋊Q8 | 2 |
| C7×A4⋊C8 | 2 |
| C7×#451 | 3 |
| C7×#216 | 4 |
| #5416 | 7 |