Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 136 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. #10620510 | C2 | direct (N × H) |
| 10. C2×Dic42 | C4 | semidirect |
| 31. Dic42 | C2×C4 | semidirect |
| 84. C2×C3×C7 | #103 | semidirect |
| 114. C3×C7 | C2×#103 | semidirect |
| 126. C2×C7 | #816 | semidirect |
| 152. C7 | C2×#816 | semidirect |
| 153. C2×C3 | #6384 | semidirect |
| 166. C3 | C2×#6384 | semidirect |
| 167. C2 | #10620510 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C22×C3×C7⋊C8 | 2 |
| #10620510 | 2 |
| C2×#6384 | 3 |
| C2×#816 | 7 |