Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10620524 | C2 | semidirect |
| 5. #10620521 | C2 | semidirect |
| 8. C2×C3⋊(C7⋊C8) | C4 | semidirect |
| 100. C3×C7 | #427 | semidirect |
| 131. C7 | #4998 | semidirect |
| 143. C3 | #89770 | 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 |
| C7×#926 | 2 |
| C3×#6489 | 2 |
| #10620524 | 2 |
| #10620521 | 2 |
| #89770 | 3 |
| #4998 | 7 |