Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 110 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. C2×C7×ΓL(1,𝔽25) | C2 | semidirect |
| 3. D3×C7×C4⋊C4 | C2 | semidirect |
| 4. C3×C7×#103 | C2 | semidirect |
| 5. C7×#835 | C2 | semidirect |
| 6. C7×#821 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 11. C7×#239 | C4 | semidirect |
| 27. C7×#103 | D3 | semidirect |
| 30. #4803 | C7 | direct (N × H) |
| 34. C3×C7×Q8 | C2×C4 | semidirect |
| 42. C7×D12 | C2×C4 | semidirect |
| 64. C2×ΓL(1,𝔽25) | C2×C7 | semidirect |
| 65. D3×C4⋊C4 | C2×C7 | semidirect |
| 66. C3×#103 | C2×C7 | semidirect |
| 67. #835 | C2×C7 | semidirect |
| 68. #821 | C2×C7 | semidirect |
| 69. #809 | C2×C7 | semidirect |
| 87. C7×Q8 | C4×D3 | semidirect |
| 104. #239 | C4×C7 | semidirect |
| 125. #103 | D3×C7 | semidirect |
| 144. C3×Q8 | C2×C4×C7 | semidirect |
| 152. D12 | C2×C4×C7 | semidirect |
| 159. C3×C7 | #417 | semidirect |
| 195. Q8 | C4×D3×C7 | semidirect |
| 210. C7 | #4803 | direct (N × H) |
| 229. C3 | C7×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#239 | 2 |
| C2×C7×ΓL(1,𝔽25) | 2 |
| D3×C7×C4⋊C4 | 2 |
| C3×C7×#103 | 2 |
| C7×#835 | 2 |
| C7×#821 | 2 |
| C7×#809 | 2 |
| C7×#417 | 3 |
| #4803 | 7 |