Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 4. #10620487 | C2 | semidirect |
| 5. C3⋊C8×Dic7 | C2 | semidirect |
| 8. C2×C3⋊(C7⋊C8) | C4 | semidirect |
| 11. C7×#208 | C4 | semidirect |
| 66. #208 | Dic7 | semidirect |
| 95. C3×C7 | #405 | semidirect |
| 124. C7 | #4997 | semidirect |
| 135. C3 | #89894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊(C7⋊C8) | 2 |
| C2×C7×#208 | 2 |
| C3×#6489 | 2 |
| #10620487 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89894 | 3 |
| #4997 | 7 |