Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
260 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 139 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. #10620646 | C2 | direct (N × H) |
| 13. C2×C3⋊(C7⋊C8) | C4 | semidirect |
| 29. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 72. C2×C3×C7 | #107 | semidirect |
| 99. C3×C7 | C2×#107 | semidirect |
| 109. C2×C7 | #807 | semidirect |
| 132. C7 | C2×#807 | semidirect |
| 133. C2×C3 | #6381 | semidirect |
| 146. C3 | C2×#6381 | semidirect |
| 147. C2 | #10620646 | direct (N × H) |
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 |
| C2×C4⋊Dic21 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| #10620646 | 2 |
| C2×#6381 | 3 |
| C2×#807 | 7 |