Finite Group DatabasebetaFinite Group Databasebeta← C4⋊C4×C22⋊ΓL(1,𝔽8) #13060771
Order 1344.
226 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 55 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. C22×C7×C4⋊C4 | C3 | semidirect |
| 6. C4×C22⋊ΓL(1,𝔽8) | C4 | semidirect |
| 27. C22×C4×C7 | C3×C4 | semidirect |
| 31. C7×C4⋊C4 | A4 | semidirect |
| 34. C22⋊ΓL(1,𝔽8) | C4⋊C4 | direct (N × H) |
| 38. C22×C4⋊C4 | ΓL(1,𝔽8) | semidirect |
| 80. C22×C7 | C3×C4⋊C4 | semidirect |
| 85. C4×C7 | C4×A4 | semidirect |
| 100. C22×C4 | C4×ΓL(1,𝔽8) | semidirect |
| 104. C4⋊C4 | C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 135. C7 | A4×C4⋊C4 | semidirect |
| 149. C22 | C4⋊C4×ΓL(1,𝔽8) | semidirect |
| 154. C4 | C4×C22⋊ΓL(1,𝔽8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C22×C7×C4⋊C4 | 3 |
| C4⋊C4×ΓL(1,𝔽8) | 4 |
| A4×C4⋊C4 | 7 |