Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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. #6433⋊C3 | C2 | semidirect |
| 3. #6409⋊C3 | C2 | semidirect |
| 5. C4×ΓL(1,𝔽8)⋊C8 | C2 | semidirect |
| 6. #89828 | C3 | semidirect |
| 15. #6433 | C2×C3 | semidirect |
| 16. #6409 | C2×C3 | semidirect |
| 18. C4×C7⋊C8 | C2×C3 | semidirect |
| 86. ΓL(1,𝔽8) | #488 | semidirect |
| 112. C7 | C3×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#124 | 2 |
| #6433⋊C3 | 2 |
| #6409⋊C3 | 2 |
| #6406⋊C3 | 2 |
| C4×ΓL(1,𝔽8)⋊C8 | 2 |
| #89828 | 3 |
| C3×#488 | 7 |