Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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. C7×#818 | C2 | semidirect |
| 3. C2×C7×C3⋊C16 | C2 | semidirect |
| 7. C3×C7×D8 | C4 | semidirect |
| 14. #4562 | C7 | direct (N × H) |
| 24. C7×D8 | Dic3 | semidirect |
| 29. #818 | C2×C7 | semidirect |
| 30. C2×C3⋊C16 | C2×C7 | semidirect |
| 48. C3×D8 | C4×C7 | semidirect |
| 73. C3×C7 | #357 | semidirect |
| 76. D8 | C7×Dic3 | semidirect |
| 98. C7 | #4562 | direct (N × H) |
| 110. C3 | C7×#357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×D8 | 2 |
| C7×#818 | 2 |
| C2×C7×C3⋊C16 | 2 |
| C7×#357 | 3 |
| #4562 | 7 |