Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×C7×H(5,𝔽2) | C2 | semidirect |
| 2. C7×#949 | C2 | semidirect |
| 3. C7×#940 | C2 | semidirect |
| 4. C7×#837 | C2 | semidirect |
| 5. C7×#833 | C2 | semidirect |
| 13. C2×C7×D12 | C22 | semidirect |
| 16. C4×C7×Dic3 | C22 | semidirect |
| 17. C7×#208 | C22 | semidirect |
| 18. C7×H(5,𝔽2) | D3 | semidirect |
| 23. #5241 | C7 | direct (N × H) |
| 27. C3×C7×Q8 | D4 | semidirect |
| 31. C3×C7×D4 | D4 | semidirect |
| 50. C3×H(5,𝔽2) | C2×C7 | semidirect |
| 51. #949 | C2×C7 | semidirect |
| 52. #940 | C2×C7 | semidirect |
| 53. #837 | C2×C7 | semidirect |
| 54. #833 | C2×C7 | semidirect |
| 69. C7×Q8 | #67 | semidirect |
| 75. C7×D4 | #67 | semidirect |
| 87. C2×D12 | C22×C7 | semidirect |
| 90. C4×Dic3 | C22×C7 | semidirect |
| 91. #208 | C22×C7 | semidirect |
| 97. H(5,𝔽2) | D3×C7 | semidirect |
| 115. C3×Q8 | C7×D4 | semidirect |
| 119. C3×D4 | C7×D4 | semidirect |
| 127. C3×C7 | #453 | semidirect |
| 157. Q8 | C7×#67 | semidirect |
| 163. D4 | C7×#67 | semidirect |
| 169. C7 | #5241 | direct (N × H) |
| 185. C3 | C7×#453 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×H(5,𝔽2) | 2 |
| C7×#949 | 2 |
| C7×#940 | 2 |
| C7×#837 | 2 |
| C7×#833 | 2 |
| C7×#453 | 3 |
| #5241 | 7 |