Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 102 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×D7×M16 | C2 | semidirect |
| 3. C3×C7×#101 | C2 | semidirect |
| 4. C3×#6410 | C2 | semidirect |
| 5. C3×#6397 | C2 | semidirect |
| 6. #89523 | C3 | direct (N × H) |
| 19. D7×M16 | C2×C3 | semidirect |
| 20. C7×#101 | C2×C3 | semidirect |
| 21. #6410 | C2×C3 | semidirect |
| 22. #6397 | C2×C3 | semidirect |
| 52. C3×#101 | D7 | semidirect |
| 96. #101 | C3×D7 | semidirect |
| 121. C3×C7 | #413 | semidirect |
| 160. C7 | C3×#413 | semidirect |
| 174. C3 | #89523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1161 | 2 |
| C3×D7×M16 | 2 |
| C3×C7×#101 | 2 |
| C3×#6410 | 2 |
| C3×#6397 | 2 |
| #89523 | 3 |
| C3×#413 | 7 |