Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C7×C22⋊Q8 | C2 | semidirect |
| 3. C2×C7×#215 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 8. C2×C3×C7×Q8 | C22 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 17. C2×C7×C3⋊C8 | C22 | semidirect |
| 20. C7×C22⋊Q8 | D3 | semidirect |
| 23. #5046 | C7 | direct (N × H) |
| 40. C2×C7×Q8 | C2×D3 | semidirect |
| 48. C7×C4⋊C4 | C2×D3 | semidirect |
| 51. C3×C22⋊Q8 | C2×C7 | semidirect |
| 52. C2×#215 | C2×C7 | semidirect |
| 53. #830 | C2×C7 | semidirect |
| 54. #809 | C2×C7 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 84. C2×C3×Q8 | C22×C7 | semidirect |
| 90. C3×C4⋊C4 | C22×C7 | semidirect |
| 93. C2×C3⋊C8 | C22×C7 | semidirect |
| 101. C22⋊Q8 | D3×C7 | semidirect |
| 110. C22×C7 | #215 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 133. C2×Q8 | C2×D3×C7 | semidirect |
| 141. C4⋊C4 | C2×D3×C7 | semidirect |
| 150. C22×C3 | C7×SD16 | semidirect |
| 175. C7 | #5046 | direct (N × H) |
| 187. C22 | C7×#215 | semidirect |
| 193. C3 | C7×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×D12 | 2 |
| C3×C7×C22⋊Q8 | 2 |
| C2×C7×#215 | 2 |
| C7×#830 | 2 |
| C7×#809 | 2 |
| C7×#450 | 3 |
| #5046 | 7 |