Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
468 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 4. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 5. ΓL(1,𝔽8)⋊#95 | C2 | semidirect |
| 6. #89722 | C3 | semidirect |
| 14. C22⋊C4×ΓL(1,𝔽8) | C4 | semidirect |
| 20. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 21. C7⋊#95 | C2×C3 | semidirect |
| 31. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 47. C7×C22⋊C4 | C3×C4 | semidirect |
| 59. C22×ΓL(1,𝔽8) | C4⋊C4 | semidirect |
| 78. C2×C4×C7 | C2×C3×C4 | semidirect |
| 112. C22×C7 | C3×C4⋊C4 | semidirect |
| 139. ΓL(1,𝔽8) | #385 | semidirect |
| 149. C22⋊C4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 186. C2×C4 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 187. C7 | C3×#385 | semidirect |
| 198. C22 | C4⋊(ΓL(1,𝔽8)⋊C4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×C22⋊C4×ΓL(1,𝔽8) | 2 |
| C2×(C22⋊Dic7)⋊C3 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| #89722 | 3 |
| C3×#385 | 7 |