Finite Group DatabasebetaFinite Group Databasebeta← C22⋊C4×C22⋊ΓL(1,𝔽8) #13060770
Order 1344.
338 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. C2×C4×C22⋊ΓL(1,𝔽8) | C2 | semidirect |
| 3. C22×C7×C22⋊C4 | C3 | semidirect |
| 5. C22×C22⋊ΓL(1,𝔽8) | C4 | semidirect |
| 10. C23×C4×C7 | C2×C3 | semidirect |
| 25. C24×C7 | C3×C4 | semidirect |
| 34. C7×C22⋊C4 | A4 | semidirect |
| 37. C22⋊ΓL(1,𝔽8) | C22⋊C4 | direct (N × H) |
| 42. C22×C22⋊C4 | ΓL(1,𝔽8) | semidirect |
| 67. C2×C4×C7 | C2×A4 | semidirect |
| 77. C23×C4 | C2×ΓL(1,𝔽8) | semidirect |
| 97. C22×C7 | C3×C22⋊C4 | semidirect |
| 98. C22×C7 | C4×A4 | semidirect |
| 113. C24 | C4×ΓL(1,𝔽8) | semidirect |
| 122. C22⋊C4 | C22⋊ΓL(1,𝔽8) | direct (N × H) |
| 159. C2×C4 | C2×C22⋊ΓL(1,𝔽8) | semidirect |
| 160. C7 | A4×C22⋊C4 | semidirect |
| 180. C22 | C22⋊C4×ΓL(1,𝔽8) | semidirect |
| 181. C22 | 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 |
|---|---|
| C23×C22⋊ΓL(1,𝔽8) | 2 |
| C2×C4×C22⋊ΓL(1,𝔽8) | 2 |
| C22×C7×C22⋊C4 | 3 |
| C22⋊C4×ΓL(1,𝔽8) | 4 |
| A4×C22⋊C4 | 7 |