Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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×ΓL(1,𝔽8)⋊C16 | C2 | semidirect |
| 3. C22⋊(C7⋊C16) | C3 | semidirect |
| 10. C2×C7⋊C16 | C2×C3 | semidirect |
| 28. C22×ΓL(1,𝔽8) | C16 | semidirect |
| 54. C22×C7 | C3×C16 | semidirect |
| 66. ΓL(1,𝔽8) | C22⋊C16 | semidirect |
| 90. C7 | C3×C22⋊C16 | semidirect |
| 97. C22 | ΓL(1,𝔽8)⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×ΓL(1,𝔽8) | 2 |
| C2×ΓL(1,𝔽8)⋊C16 | 2 |
| C22⋊(C7⋊C16) | 3 |
| C3×C22⋊C16 | 7 |