Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
580 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 236 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. ΓL(1,𝔽8)×C4⋊Q8 | C2 | semidirect |
| 3. #6507⋊C3 | C2 | semidirect |
| 5. #6451⋊C3 | C2 | semidirect |
| 7. #6432⋊C3 | C2 | semidirect |
| 8. D7×C4⋊Q8 | C3 | semidirect |
| 23. C7×C4⋊Q8 | C2×C3 | semidirect |
| 24. #6507 | C2×C3 | semidirect |
| 26. #6451 | C2×C3 | semidirect |
| 28. #6432 | C2×C3 | semidirect |
| 40. C4×AGL(1,𝔽7) | Q8 | semidirect |
| 68. C4×ΓL(1,𝔽8) | C2×Q8 | semidirect |
| 71. ΓL(1,𝔽8)⋊C4 | C2×Q8 | semidirect |
| 83. C4×D7 | C3×Q8 | semidirect |
| 101. AGL(1,𝔽7) | C4⋊Q8 | direct (N × H) |
| 106. C4⋊Q8 | AGL(1,𝔽7) | direct (N × H) |
| 114. C4×C7 | C2×C3×Q8 | semidirect |
| 117. Dic7 | C2×C3×Q8 | semidirect |
| 131. ΓL(1,𝔽8) | C2×C4⋊Q8 | semidirect |
| 147. D7 | C3×C4⋊Q8 | semidirect |
| 170. C7 | C2×C3×C4⋊Q8 | semidirect |
| 182. C4 | Q8×AGL(1,𝔽7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×C4⋊Q8 | 2 |
| #6507⋊C3 | 2 |
| C4⋊C4×AGL(1,𝔽7) | 2 |
| #6451⋊C3 | 2 |
| C42×AGL(1,𝔽7) | 2 |
| #6432⋊C3 | 2 |
| D7×C4⋊Q8 | 3 |
| C2×C3×C4⋊Q8 | 7 |