Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 1. C22×C3×C7×D4 | C2 | semidirect |
| 2. C2×C7×#213 | C2 | semidirect |
| 3. C7×#930 | C2 | semidirect |
| 4. C7×#832 | C2 | semidirect |
| 5. C7×#830 | C2 | semidirect |
| 13. C2×C7×D12 | C22 | semidirect |
| 16. C7×C4⋊Dic3 | C22 | semidirect |
| 17. C2×C7×C3⋊C8 | C22 | semidirect |
| 18. C22×C7×D4 | D3 | semidirect |
| 23. #5217 | C7 | direct (N × H) |
| 32. C3×C7×D4 | D4 | semidirect |
| 51. C22×C3×D4 | C2×C7 | semidirect |
| 52. C2×#213 | C2×C7 | semidirect |
| 53. #930 | C2×C7 | semidirect |
| 54. #832 | C2×C7 | semidirect |
| 55. #830 | C2×C7 | semidirect |
| 62. C22×C3×C7 | D8 | semidirect |
| 81. C7×D4 | #67 | semidirect |
| 93. C2×D12 | C22×C7 | semidirect |
| 96. C4⋊Dic3 | C22×C7 | semidirect |
| 97. C2×C3⋊C8 | C22×C7 | semidirect |
| 104. C22×D4 | D3×C7 | semidirect |
| 118. C22×C7 | #213 | semidirect |
| 131. C3×D4 | C7×D4 | semidirect |
| 139. C3×C7 | #447 | semidirect |
| 163. C22×C3 | C7×D8 | semidirect |
| 181. D4 | C7×#67 | semidirect |
| 187. C7 | #5217 | direct (N × H) |
| 203. C22 | C7×#213 | semidirect |
| 208. C3 | C7×#447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C7×D4 | 2 |
| C2×C7×#213 | 2 |
| C7×#930 | 2 |
| C7×#832 | 2 |
| C7×#830 | 2 |
| C7×#447 | 3 |
| #5217 | 7 |