Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 126 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×C3×C7×M16 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C7×#823 | C2 | direct (N × H) |
| 15. C3×C7×M16 | C22 | semidirect |
| 18. C7×#208 | C22 | semidirect |
| 22. C2×C7×M16 | D3 | semidirect |
| 24. C2×#823 | C7 | direct (N × H) |
| 53. C7×M16 | C2×D3 | semidirect |
| 57. C2×C3×M16 | C2×C7 | semidirect |
| 58. C2×#208 | C2×C7 | semidirect |
| 59. #823 | C2×C7 | direct (N × H) |
| 99. C3×M16 | C22×C7 | semidirect |
| 102. #208 | C22×C7 | semidirect |
| 106. C2×C3×C7 | #100 | semidirect |
| 111. C2×M16 | D3×C7 | semidirect |
| 142. C3×C7 | C2×#100 | semidirect |
| 154. M16 | C2×D3×C7 | semidirect |
| 160. C2×C7 | #823 | direct (N × H) |
| 191. C7 | C2×#823 | direct (N × H) |
| 194. C2×C3 | C7×#100 | semidirect |
| 209. C3 | C2×C7×#100 | semidirect |
| 213. C2 | C7×#823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C2×C3×C7×M16 | 2 |
| C2×C7×#208 | 2 |
| C7×#823 | 2 |
| C2×C7×#100 | 3 |
| C2×#823 | 7 |