Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
596 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 296 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. C22×ΓL(1,𝔽8)⋊C8 | C2 | semidirect |
| 4. C2×#1131⋊C3 | C2 | direct (N × H) |
| 5. C22×#1131 | C3 | semidirect |
| 11. C2×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 12. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 13. #1131⋊C3 | C22 | direct (N × H) |
| 15. C22×C7×C8 | C2×C3 | semidirect |
| 16. C22×C7⋊C8 | C2×C3 | semidirect |
| 17. C2×#1131 | C2×C3 | semidirect |
| 27. C8×ΓL(1,𝔽8) | C23 | semidirect |
| 28. ΓL(1,𝔽8)⋊C8 | C23 | semidirect |
| 34. C2×C7×C8 | C22×C3 | semidirect |
| 35. C2×C7⋊C8 | C22×C3 | semidirect |
| 36. #1131 | C22×C3 | semidirect |
| 41. C22×ΓL(1,𝔽8) | M16 | semidirect |
| 57. C7×C8 | C23×C3 | semidirect |
| 58. C7⋊C8 | C23×C3 | semidirect |
| 67. C2×ΓL(1,𝔽8) | C2×M16 | semidirect |
| 73. C22×C8 | AGL(1,𝔽7) | semidirect |
| 74. C22×C7 | C3×M16 | semidirect |
| 91. ΓL(1,𝔽8) | C22×M16 | semidirect |
| 99. C2×C8 | C2×AGL(1,𝔽7) | semidirect |
| 100. C2×C7 | C2×C3×M16 | semidirect |
| 119. C8 | C22×AGL(1,𝔽7) | semidirect |
| 120. C7 | C22×C3×M16 | semidirect |
| 126. C22 | #1131⋊C3 | direct (N × H) |
| 133. C2 | C2×#1131⋊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 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| C2×#1131⋊C3 | 2 |
| C22×#1131 | 3 |
| C22×C3×M16 | 7 |