Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 204 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 |
|---|---|---|
| 4. #6396⋊C3 | C2 | semidirect |
| 5. #89896 | C3 | semidirect |
| 19. #6396 | C2×C3 | semidirect |
| 100. ΓL(1,𝔽8) | #430 | semidirect |
| 133. C7 | C3×#430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×ΓL(1,𝔽8) | 2 |
| C2×#1136⋊C3 | 2 |
| #6396⋊C3 | 2 |
| #89896 | 3 |
| C3×#430 | 7 |