Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
620 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 282 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. C4×Q8×ΓL(1,𝔽8) | C2 | semidirect |
| 3. Q8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 4. #6456⋊C3 | C2 | semidirect |
| 5. #6455⋊C3 | C2 | semidirect |
| 6. C4×C4⋊AGL(1,𝔽7) | C2 | semidirect |
| 7. C42×AGL(1,𝔽7) | C2 | semidirect |
| 8. C4×#1161 | C3 | semidirect |
| 10. #66659 | C4 | direct (N × H) |
| 23. C4×C7×Q8 | C2×C3 | semidirect |
| 24. Q8×Dic7 | C2×C3 | semidirect |
| 25. #6456 | C2×C3 | semidirect |
| 26. #6455 | C2×C3 | semidirect |
| 27. C4×D28 | C2×C3 | semidirect |
| 28. C42×D7 | C2×C3 | semidirect |
| 31. Q8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 38. C4⋊AGL(1,𝔽7) | C2×C4 | semidirect |
| 41. C4×AGL(1,𝔽7) | C2×C4 | semidirect |
| 43. #1161 | C3×C4 | semidirect |
| 68. C4×ΓL(1,𝔽8) | #41 | semidirect |
| 71. ΓL(1,𝔽8)⋊C4 | #41 | semidirect |
| 74. C7×Q8 | C2×C3×C4 | semidirect |
| 81. D28 | C2×C3×C4 | semidirect |
| 84. C4×D7 | C2×C3×C4 | semidirect |
| 104. C4×Q8 | AGL(1,𝔽7) | semidirect |
| 115. C4×C7 | C3×#41 | semidirect |
| 118. Dic7 | C3×#41 | semidirect |
| 131. ΓL(1,𝔽8) | C4×#41 | semidirect |
| 160. Q8 | C4×AGL(1,𝔽7) | semidirect |
| 171. C7 | C3×C4×#41 | semidirect |
| 185. C4 | #66659 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66659 | 2 |
| C4×Q8×ΓL(1,𝔽8) | 2 |
| Q8×ΓL(1,𝔽8)⋊C4 | 2 |
| #6456⋊C3 | 2 |
| #6455⋊C3 | 2 |
| C4×C4⋊AGL(1,𝔽7) | 2 |
| C42×AGL(1,𝔽7) | 2 |
| C4×#1161 | 3 |
| C3×C4×#41 | 7 |