Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 67 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. #10621353 | C2 | semidirect |
| 3. #10620674 | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 86. C3×C7 | #488 | semidirect |
| 112. C7 | #5056 | semidirect |
| 123. C3 | #89828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#124 | 2 |
| #10621353 | 2 |
| #10620674 | 2 |
| #10620671 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89828 | 3 |
| #5056 | 7 |