Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 140 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×C42×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×(C2×AGL(1,𝔽7))⋊C4 | C2 | semidirect |
| 4. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 5. #89711 | C3 | semidirect |
| 12. C2×C4⋊AGL(1,𝔽7) | C4 | semidirect |
| 17. C2×C42×C7 | C2×C3 | semidirect |
| 18. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 19. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 32. C2×C4×ΓL(1,𝔽8) | D4 | semidirect |
| 42. C2×D28 | C3×C4 | semidirect |
| 61. C4×ΓL(1,𝔽8) | C22⋊C4 | semidirect |
| 75. C2×C4×C7 | C3×D4 | semidirect |
| 98. C2×C42 | AGL(1,𝔽7) | semidirect |
| 110. C4×C7 | C3×C22⋊C4 | semidirect |
| 127. ΓL(1,𝔽8) | #390 | semidirect |
| 170. C2×C4 | C4⋊AGL(1,𝔽7) | semidirect |
| 172. C7 | C3×#390 | semidirect |
| 191. C4 | (C2×AGL(1,𝔽7))⋊C4 | semidirect |
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 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| C2×(C2×AGL(1,𝔽7))⋊C4 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| #89711 | 3 |
| C3×#390 | 7 |