Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #6392⋊C3 | C2 | semidirect |
| 4. #6391⋊C3 | C2 | semidirect |
| 5. #89878 | C3 | semidirect |
| 7. C2×C8×ΓL(1,𝔽8) | C4 | semidirect |
| 15. #6392 | C2×C3 | semidirect |
| 16. #6391 | C2×C3 | semidirect |
| 27. C2×C7×C8 | C3×C4 | semidirect |
| 82. ΓL(1,𝔽8) | #427 | semidirect |
| 84. C2×C8 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 108. C7 | C3×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×ΓL(1,𝔽8) | 2 |
| #6489⋊C3 | 2 |
| #6392⋊C3 | 2 |
| #6391⋊C3 | 2 |
| #89878 | 3 |
| C3×#427 | 7 |