Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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. C22×C8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 4. #6395⋊C3 | C2 | direct (N × H) |
| 5. C2×#6395 | C3 | semidirect |
| 11. C2×C4⋊AGL(1,𝔽7) | C4 | semidirect |
| 14. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 16. C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | semidirect |
| 18. C22×C7×C8 | C2×C3 | semidirect |
| 19. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 20. #6395 | C2×C3 | semidirect |
| 35. C4⋊AGL(1,𝔽7) | C2×C4 | semidirect |
| 42. C2×D28 | C3×C4 | semidirect |
| 45. C2×C7×C8 | C22×C3 | semidirect |
| 47. C4⋊Dic7 | C22×C3 | semidirect |
| 78. D28 | C2×C3×C4 | semidirect |
| 91. C2×ΓL(1,𝔽8) | #102 | semidirect |
| 97. C22×C8 | AGL(1,𝔽7) | semidirect |
| 127. ΓL(1,𝔽8) | C2×#102 | semidirect |
| 136. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 139. C2×C7 | C3×#102 | semidirect |
| 171. C7 | C2×C3×#102 | semidirect |
| 191. C2 | #6395⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊AGL(1,𝔽7) | 2 |
| C22×C8×ΓL(1,𝔽8) | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| #6395⋊C3 | 2 |
| C2×#6395 | 3 |
| C2×C3×#102 | 7 |