Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
392 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 162 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. #6507⋊C3 | C2 | semidirect |
| 4. #6442⋊C3 | C2 | semidirect |
| 5. #6441⋊C3 | C2 | semidirect |
| 6. #6433⋊C3 | C2 | semidirect |
| 7. #90363 | C3 | semidirect |
| 23. #6507 | C2×C3 | semidirect |
| 25. #6442 | C2×C3 | semidirect |
| 26. #6441 | C2×C3 | semidirect |
| 27. #6433 | C2×C3 | semidirect |
| 119. ΓL(1,𝔽8) | #563 | semidirect |
| 155. C7 | C3×#563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#124 | 2 |
| #6507⋊C3 | 2 |
| #6498⋊C3 | 2 |
| #6442⋊C3 | 2 |
| #6441⋊C3 | 2 |
| #6433⋊C3 | 2 |
| #90363 | 3 |
| C3×#563 | 7 |