Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
436 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 3. C7×C3⋊#95 | C2 | semidirect |
| 7. C22×C3×C4×C7 | C4 | semidirect |
| 14. #5211 | C7 | direct (N × H) |
| 27. C22×C4×C7 | Dic3 | semidirect |
| 32. C3⋊#95 | C2×C7 | semidirect |
| 53. C22×C3×C4 | C4×C7 | semidirect |
| 81. C3×C7 | #381 | semidirect |
| 85. C22×C4 | C7×Dic3 | semidirect |
| 109. C7 | #5211 | direct (N × H) |
| 122. C3 | C7×#381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C7 | 2 |
| C2×C7×#217 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#381 | 3 |
| #5211 | 7 |