Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
300 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 98 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. C2×M16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. C2×#1136⋊C3 | C2 | semidirect |
| 4. #6398⋊C3 | C2 | semidirect |
| 5. #6397⋊C3 | C2 | semidirect |
| 6. #89904 | C3 | semidirect |
| 23. C2×C7×M16 | C2×C3 | semidirect |
| 24. C2×#1136 | C2×C3 | semidirect |
| 25. #6398 | C2×C3 | semidirect |
| 26. #6397 | C2×C3 | semidirect |
| 120. C2×M16 | AGL(1,𝔽7) | semidirect |
| 153. ΓL(1,𝔽8) | #413 | semidirect |
| 204. C7 | C3×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C2×M16×ΓL(1,𝔽8) | 2 |
| C2×#1136⋊C3 | 2 |
| #6398⋊C3 | 2 |
| #6397⋊C3 | 2 |
| #89904 | 3 |
| C3×#413 | 7 |