Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
296 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 90 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×Dic12 | C2 | semidirect |
| 5. C3×C7×#103 | C2 | semidirect |
| 7. C7×#810 | C2 | semidirect |
| 29. C7×#103 | D3 | semidirect |
| 31. #4809 | C7 | direct (N × H) |
| 67. C2×#216 | C2×C7 | semidirect |
| 68. C2×Dic12 | C2×C7 | semidirect |
| 70. C3×#103 | C2×C7 | semidirect |
| 72. #810 | C2×C7 | semidirect |
| 76. C2×D3×C7 | Q16 | semidirect |
| 128. #103 | D3×C7 | semidirect |
| 160. C3×C7 | #451 | semidirect |
| 183. C2×D3 | C7×Q16 | semidirect |
| 210. C7 | #4809 | direct (N × H) |
| 226. C3 | C7×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×C7×#216 | 2 |
| C2×C7×Dic12 | 2 |
| C7×#897 | 2 |
| C3×C7×#103 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#810 | 2 |
| C7×#451 | 3 |
| #4809 | 7 |