Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 2. C2×C7×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C3×C7×C22⋊C8 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 5. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 15. C2×C3×C7×C8 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 22. C7×C22⋊C8 | D3 | semidirect |
| 23. #4726 | C7 | direct (N × H) |
| 52. C2×C7×C8 | C2×D3 | semidirect |
| 54. C2×ΓL(1,𝔽25) | C2×C7 | semidirect |
| 55. C3×C22⋊C8 | C2×C7 | semidirect |
| 56. #830 | C2×C7 | semidirect |
| 57. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 60. C22×C3×C7 | M16 | semidirect |
| 68. C2×D3×C7 | M16 | semidirect |
| 100. C2×C3×C8 | C22×C7 | semidirect |
| 101. C2×C3⋊C8 | C22×C7 | semidirect |
| 113. C22⋊C8 | D3×C7 | semidirect |
| 123. C22×C7 | ΓL(1,𝔽25) | semidirect |
| 147. C3×C7 | #407 | semidirect |
| 158. C2×C8 | C2×D3×C7 | semidirect |
| 167. C22×C3 | C7×M16 | semidirect |
| 175. C2×D3 | C7×M16 | semidirect |
| 198. C7 | #4726 | direct (N × H) |
| 214. C22 | C7×ΓL(1,𝔽25) | semidirect |
| 220. C3 | C7×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3×C7 | 2 |
| C2×C7×ΓL(1,𝔽25) | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×#830 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#407 | 3 |
| #4726 | 7 |