Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 2. C7×#803 | C2 | semidirect |
| 3. C3×C4×C7⋊C8 | C2 | semidirect |
| 4. #10620518 | C2 | semidirect |
| 18. C4×C7⋊C8 | D3 | semidirect |
| 39. #803 | D7 | semidirect |
| 86. C3×C7 | #433 | semidirect |
| 112. C7 | #4690 | semidirect |
| 123. C3 | #89481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621355 | 2 |
| C7×#803 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #10620518 | 2 |
| #10620492 | 2 |
| #89481 | 3 |
| #4690 | 7 |