Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 166 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. #89746 | C3 | direct (N × H) |
| 12. C2×C3×Dic14 | C4 | semidirect |
| 31. C2×C3×Dic7 | Q8 | semidirect |
| 39. C2×Dic14 | C3×C4 | semidirect |
| 67. C2×Dic7 | C3×Q8 | semidirect |
| 109. C3×C7 | #391 | semidirect |
| 146. C7 | C3×#391 | semidirect |
| 161. C3 | #89746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C3×C7⋊#95 | 2 |
| #89746 | 3 |
| C3×#391 | 7 |