Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
388 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 12. C4×Dic21 | C4 | semidirect |
| 13. #66577 | C4 | semidirect |
| 54. Dic21 | C42 | semidirect |
| 55. Dic21 | C4⋊C4 | semidirect |
| 115. C3×C7 | C4×C4⋊C4 | semidirect |
| 153. C7 | #4649 | semidirect |
| 169. C3 | #89421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C2×#66577 | 2 |
| C2×Dic3×Dic7 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C7⋊#95 | 2 |
| #89421 | 3 |
| #4649 | 7 |