Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 4. C2×#1144⋊C3 | C2 | semidirect |
| 5. #6410⋊C3 | C2 | semidirect |
| 6. #6398⋊C3 | C2 | semidirect |
| 7. #6396⋊C3 | C2 | semidirect |
| 8. #89976 | C3 | semidirect |
| 27. C2×#1144 | C2×C3 | semidirect |
| 28. #6410 | C2×C3 | semidirect |
| 29. #6398 | C2×C3 | semidirect |
| 30. #6396 | C2×C3 | semidirect |
| 142. ΓL(1,𝔽8) | #473 | semidirect |
| 184. C7 | C3×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#137 | 2 |
| #6514⋊C3 | 2 |
| #10620784 | 2 |
| C2×#1144⋊C3 | 2 |
| #6410⋊C3 | 2 |
| #6398⋊C3 | 2 |
| #6396⋊C3 | 2 |
| #89976 | 3 |
| C3×#473 | 7 |