Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 142 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×#926 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 9. C2×C3×C7×D4 | C4 | semidirect |
| 13. C7×C4⋊Dic3 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 21. #5215 | C7 | direct (N × H) |
| 38. C2×C7×D4 | Dic3 | semidirect |
| 47. #926 | C2×C7 | semidirect |
| 48. C2×#208 | C2×C7 | semidirect |
| 49. #832 | C2×C7 | semidirect |
| 77. C2×C3×D4 | C4×C7 | semidirect |
| 81. C4⋊Dic3 | C22×C7 | semidirect |
| 84. C2×C3⋊C8 | C22×C7 | semidirect |
| 116. C3×C7 | #418 | semidirect |
| 120. C2×D4 | C7×Dic3 | semidirect |
| 155. C7 | #5215 | direct (N × H) |
| 170. C3 | C7×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C7×#926 | 2 |
| C2×C7×#208 | 2 |
| C7×#832 | 2 |
| C7×#418 | 3 |
| #5215 | 7 |