Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
444 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 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. #6453⋊C3 | C2 | semidirect |
| 5. #6451⋊C3 | C2 | semidirect |
| 7. C4×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 8. #90208 | C3 | semidirect |
| 27. #6453 | C2×C3 | semidirect |
| 28. #6451 | C2×C3 | semidirect |
| 30. C4×Dic14 | C2×C3 | semidirect |
| 33. C2×C4×ΓL(1,𝔽8) | Q8 | semidirect |
| 75. C2×C4×C7 | C3×Q8 | semidirect |
| 128. ΓL(1,𝔽8) | #533 | semidirect |
| 162. C2×C4 | ΓL(1,𝔽8)⋊Q8 | semidirect |
| 166. C7 | C3×#533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#117 | 2 |
| #6489⋊C3 | 2 |
| C2×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| #6453⋊C3 | 2 |
| #6451⋊C3 | 2 |
| #6441⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊Q8 | 2 |
| #90208 | 3 |
| C3×#533 | 7 |