Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
388 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 13. #66629 | C4 | direct (N × H) |
| 15. C4×Dic21 | C4 | semidirect |
| 56. C3×C4×C7 | C4⋊C4 | semidirect |
| 59. Dic21 | C42 | semidirect |
| 100. C4×C7 | Dic3⋊C4 | semidirect |
| 118. C3×C7 | C4×C4⋊C4 | semidirect |
| 139. C3×C4 | Dic7⋊C4 | semidirect |
| 157. C7 | C4×Dic3⋊C4 | semidirect |
| 172. C4 | #66629 | direct (N × H) |
| 173. C3 | C4×Dic7⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×#66629 | 2 |
| C2×C4×Dic21 | 2 |
| #10620670 | 2 |
| C4×Dic7⋊C4 | 3 |
| C4×Dic3⋊C4 | 7 |