Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 107 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. #10620647 | C2 | semidirect |
| 5. #10620646 | C2 | semidirect |
| 15. #66627 | C4 | semidirect |
| 32. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 108. C3×C7 | #428 | semidirect |
| 143. C7 | #4964 | semidirect |
| 158. C3 | #89736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| #10621409 | 2 |
| C2×#66627 | 2 |
| #10620647 | 2 |
| #10620646 | 2 |
| #89736 | 3 |
| #4964 | 7 |