Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 190 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 |
|---|---|---|
| 5. #89748 | C3 | direct (N × H) |
| 13. C3×C4×Dic7 | C4 | semidirect |
| 37. C4×Dic7 | C3×C4 | semidirect |
| 48. C3×C4×C7 | C4⋊C4 | semidirect |
| 50. C3×Dic7 | C4⋊C4 | semidirect |
| 86. C4×C7 | C3×C4⋊C4 | semidirect |
| 88. Dic7 | C3×C4⋊C4 | semidirect |
| 100. C3×C7 | #384 | semidirect |
| 122. C3×C4 | Dic7⋊C4 | semidirect |
| 134. C7 | C3×#384 | semidirect |
| 148. C4 | C3×Dic7⋊C4 | semidirect |
| 149. C3 | #89748 | 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×C3×C4⋊Dic7 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×C3×C4×Dic7 | 2 |
| #89748 | 3 |
| C3×#384 | 7 |