Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
196 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. C7×#343 | C3 | semidirect |
| 7. M16×ΓL(1,𝔽8) | C4 | semidirect |
| 24. C7×M16 | C3×C4 | semidirect |
| 37. #343 | ΓL(1,𝔽8) | direct (N × H) |
| 75. ΓL(1,𝔽8) | #343 | direct (N × H) |
| 79. M16 | C4×ΓL(1,𝔽8) | semidirect |
| 103. C7 | C3×#343 | 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×C4⋊C4×ΓL(1,𝔽8) | 2 |
| C7×#343 | 3 |
| C3×#343 | 7 |