Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
540 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 3. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 4. #6460⋊C3 | C2 | semidirect |
| 5. #6449⋊C3 | C2 | semidirect |
| 6. #6438⋊C3 | C2 | semidirect |
| 7. #6432⋊C3 | C2 | semidirect |
| 8. #90217 | C3 | semidirect |
| 25. C22×Dic14 | C2×C3 | semidirect |
| 26. C7×#117 | C2×C3 | semidirect |
| 27. #6460 | C2×C3 | semidirect |
| 28. #6449 | C2×C3 | semidirect |
| 29. #6438 | C2×C3 | semidirect |
| 30. #6432 | C2×C3 | semidirect |
| 120. #117 | AGL(1,𝔽7) | semidirect |
| 146. ΓL(1,𝔽8) | #536 | semidirect |
| 191. C7 | C3×#536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C22×ΓL(1,𝔽8)⋊Q8 | 2 |
| ΓL(1,𝔽8)×#117 | 2 |
| #6460⋊C3 | 2 |
| #6449⋊C3 | 2 |
| #6438⋊C3 | 2 |
| #6432⋊C3 | 2 |
| #90217 | 3 |
| C3×#536 | 7 |