Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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. C7×Q8×Dic3 | C2 | semidirect |
| 4. C3×C7×#103 | C2 | semidirect |
| 6. C7×#815 | C2 | semidirect |
| 7. C7×#807 | C2 | semidirect |
| 14. C7×#215 | C4 | semidirect |
| 25. C7×#103 | D3 | semidirect |
| 28. #4817 | C7 | direct (N × H) |
| 31. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C7×C3⋊C8 | C2×C4 | semidirect |
| 55. Q8×Dic3 | C2×C7 | semidirect |
| 58. C3×#103 | C2×C7 | semidirect |
| 60. #815 | C2×C7 | semidirect |
| 61. #807 | C2×C7 | semidirect |
| 76. C7×Q8 | C4×D3 | semidirect |
| 93. #215 | C4×C7 | semidirect |
| 108. #103 | D3×C7 | semidirect |
| 124. C3×Q8 | C2×C4×C7 | semidirect |
| 135. C3⋊C8 | C2×C4×C7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 166. Q8 | C4×D3×C7 | semidirect |
| 178. C7 | #4817 | direct (N × H) |
| 194. C3 | C7×#440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×Dic3 | 2 |
| C2×C7×#215 | 2 |
| C7×#893 | 2 |
| C3×C7×#103 | 2 |
| C7×#821 | 2 |
| C7×#815 | 2 |
| C7×#807 | 2 |
| C7×#440 | 3 |
| #4817 | 7 |