Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 76 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. #6432⋊C3 | C2 | semidirect |
| 4. #6384⋊C3 | C2 | semidirect |
| 5. C4⋊(ΓL(1,𝔽8)⋊C8) | C2 | semidirect |
| 6. #89791 | C3 | semidirect |
| 19. #6432 | C2×C3 | semidirect |
| 20. #6384 | C2×C3 | semidirect |
| 21. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 56. C4×ΓL(1,𝔽8) | SD16 | semidirect |
| 98. C4×C7 | C3×SD16 | semidirect |
| 114. ΓL(1,𝔽8) | #461 | semidirect |
| 151. C7 | C3×#461 | semidirect |
| 163. C4 | #1142⋊C3 | 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 |
| C2×#1142⋊C3 | 2 |
| #6432⋊C3 | 2 |
| #6384⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89791 | 3 |
| C3×#461 | 7 |