Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
| 5. #6382⋊C3 | C2 | semidirect |
| 6. #6381⋊C3 | C2 | semidirect |
| 7. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 8. #89781 | C3 | semidirect |
| 21. #6433 | C2×C3 | semidirect |
| 24. #6382 | C2×C3 | semidirect |
| 25. #6381 | C2×C3 | semidirect |
| 26. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 127. ΓL(1,𝔽8) | #478 | semidirect |
| 166. C7 | C3×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×ΓL(1,𝔽8) | 2 |
| #6433⋊C3 | 2 |
| #6406⋊C3 | 2 |
| #6382⋊C3 | 2 |
| #6381⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89781 | 3 |
| C3×#478 | 7 |