Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. C2×C7×#216 | C2 | semidirect |
| 5. C7×#836 | C2 | semidirect |
| 6. C7×#824 | C2 | semidirect |
| 7. C7×#822 | C2 | semidirect |
| 31. #5204 | C7 | direct (N × H) |
| 66. C2×#216 | C2×C7 | semidirect |
| 67. #836 | C2×C7 | semidirect |
| 68. #824 | C2×C7 | semidirect |
| 69. #822 | C2×C7 | semidirect |
| 142. C3×C7 | #473 | semidirect |
| 184. C7 | #5204 | direct (N × H) |
| 195. C3 | C7×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#137 | 2 |
| C7×#951 | 2 |
| C7×#948 | 2 |
| C2×C7×#216 | 2 |
| C7×#836 | 2 |
| C7×#824 | 2 |
| C7×#822 | 2 |
| C7×#473 | 3 |
| #5204 | 7 |