Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 2. C3×#6432 | C2 | semidirect |
| 3. C3×#6406 | C2 | semidirect |
| 4. C3×C4×C7⋊C8 | C2 | semidirect |
| 5. #89842 | C3 | direct (N × H) |
| 15. #6432 | C2×C3 | semidirect |
| 16. #6406 | C2×C3 | semidirect |
| 17. C4×C7⋊C8 | C2×C3 | semidirect |
| 94. C3×C7 | #486 | semidirect |
| 125. C7 | C3×#486 | semidirect |
| 138. C3 | #89842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C3×#6432 | 2 |
| C3×#6406 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89842 | 3 |
| C3×#486 | 7 |