Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
304 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 94 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×#216 | C2 | semidirect |
| 3. C2×C7×#214 | C2 | semidirect |
| 4. C7×#924 | C2 | semidirect |
| 5. C7×#835 | C2 | semidirect |
| 6. C7×#832 | C2 | semidirect |
| 7. C7×#830 | C2 | semidirect |
| 31. #5239 | C7 | direct (N × H) |
| 67. C2×#216 | C2×C7 | semidirect |
| 68. C2×#214 | C2×C7 | semidirect |
| 69. #924 | C2×C7 | semidirect |
| 70. #835 | C2×C7 | semidirect |
| 71. #832 | C2×C7 | semidirect |
| 72. #830 | C2×C7 | semidirect |
| 165. C3×C7 | #452 | semidirect |
| 218. C7 | #5239 | direct (N × H) |
| 237. C3 | C7×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×#214 | 2 |
| C7×#924 | 2 |
| C7×#835 | 2 |
| C7×#832 | 2 |
| C7×#830 | 2 |
| C7×#452 | 3 |
| #5239 | 7 |