Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 228 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 |
| 5. C7×#835 | C2 | semidirect |
| 6. C7×#810 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 29. #5051 | C7 | direct (N × H) |
| 59. C2×#216 | C2×C7 | semidirect |
| 62. #835 | C2×C7 | semidirect |
| 63. #810 | C2×C7 | semidirect |
| 64. #807 | C2×C7 | semidirect |
| 67. C22×C3×C7 | Q16 | semidirect |
| 118. C22×C7 | #216 | semidirect |
| 142. C3×C7 | #467 | semidirect |
| 162. C22×C3 | C7×Q16 | semidirect |
| 186. C7 | #5051 | direct (N × H) |
| 193. C22 | C7×#216 | semidirect |
| 202. C3 | C7×#467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C22⋊Q8 | 2 |
| C2×C7×#216 | 2 |
| C7×#924 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#835 | 2 |
| C7×#810 | 2 |
| C7×#807 | 2 |
| C7×#467 | 3 |
| #5051 | 7 |