Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 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×#1144⋊C3 | C2 | semidirect |
| 4. #6432⋊C3 | C2 | semidirect |
| 5. #6377⋊C3 | C2 | semidirect |
| 6. #89832 | C3 | semidirect |
| 17. C2×#1144 | C2×C3 | semidirect |
| 19. #6432 | C2×C3 | semidirect |
| 20. #6377 | C2×C3 | semidirect |
| 98. ΓL(1,𝔽8) | #497 | semidirect |
| 128. C7 | C3×#497 | 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 |
| C2×#1144⋊C3 | 2 |
| C2×#1142⋊C3 | 2 |
| #6432⋊C3 | 2 |
| #6377⋊C3 | 2 |
| #89832 | 3 |
| C3×#497 | 7 |