Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
1012 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1012 conjugacy classes of subgroups — too many to draw. Only its 238 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. C2×C7×#217 | C2 | semidirect |
| 5. C24×C3×C7 | C4 | semidirect |
| 7. C22×C7×Dic3 | C22 | semidirect |
| 11. #5247 | C7 | direct (N × H) |
| 20. C24×C7 | Dic3 | semidirect |
| 25. C2×#217 | C2×C7 | semidirect |
| 29. C22×C3×C7 | C22⋊C4 | semidirect |
| 42. C24×C3 | C4×C7 | semidirect |
| 44. C22×Dic3 | C22×C7 | semidirect |
| 54. C22×C7 | #217 | semidirect |
| 65. C3×C7 | #379 | semidirect |
| 67. C24 | C7×Dic3 | semidirect |
| 77. C22×C3 | C7×C22⋊C4 | semidirect |
| 88. C7 | #5247 | direct (N × H) |
| 95. C22 | C7×#217 | semidirect |
| 99. C3 | C7×#379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C3×C7 | 2 |
| C2×C7×#217 | 2 |
| C7×#379 | 3 |
| #5247 | 7 |