Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
356 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 156 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. #89420 | C3 | semidirect |
| 8. C4×ΓL(1,𝔽8)⋊C4 | C4 | semidirect |
| 23. C4×Dic7 | C3×C4 | semidirect |
| 64. ΓL(1,𝔽8) | #376 | semidirect |
| 85. C7 | C3×#376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| ΓL(1,𝔽8)×#95 | 2 |
| ΓL(1,𝔽8)⋊#95 | 2 |
| #89420 | 3 |
| C3×#376 | 7 |