Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C3×C7×C4⋊C8 | C2 | semidirect |
| 4. C7×Dic3⋊C8 | C2 | semidirect |
| 5. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 21. C7×C4⋊C8 | D3 | semidirect |
| 22. #4837 | C7 | direct (N × H) |
| 48. C3×C4⋊C8 | C2×C7 | semidirect |
| 49. Dic3⋊C8 | C2×C7 | semidirect |
| 50. C4⋊(C3⋊C8) | C2×C7 | semidirect |
| 56. C3×C4×C7 | M16 | semidirect |
| 61. C7×Dic3 | M16 | semidirect |
| 94. C4⋊C8 | D3×C7 | semidirect |
| 103. C4×C7 | ΓL(1,𝔽25) | semidirect |
| 119. C3×C7 | #423 | semidirect |
| 139. C3×C4 | C7×M16 | semidirect |
| 144. Dic3 | C7×M16 | semidirect |
| 158. C7 | #4837 | direct (N × H) |
| 171. C4 | C7×ΓL(1,𝔽25) | semidirect |
| 174. C3 | C7×#423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×ΓL(1,𝔽25) | 2 |
| C42×D3×C7 | 2 |
| C3×C7×C4⋊C8 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#423 | 3 |
| #4837 | 7 |