Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
128 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 54 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. #89342 | C3 | semidirect |
| 75. ΓL(1,𝔽8) | #332 | semidirect |
| 100. C7 | C3×#332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×C4⋊Q8 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊C8) | 2 |
| #89342 | 3 |
| C3×#332 | 7 |