Finite Group DatabasebetaFinite Group Databasebeta← C22×(ΓL(1,𝔽8)⋊C4)⋊C4 #13057517
Order 1344.
836 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 416 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. C2×(ΓL(1,𝔽8)⋊C4)⋊C4 | C2 | direct (N × H) |
| 5. C22×Dic7⋊C4 | C3 | semidirect |
| 10. C22×ΓL(1,𝔽8)⋊C4 | C4 | semidirect |
| 13. (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | direct (N × H) |
| 17. C2×Dic7⋊C4 | C2×C3 | semidirect |
| 26. C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | semidirect |
| 33. C22×Dic7 | C3×C4 | semidirect |
| 36. Dic7⋊C4 | C22×C3 | semidirect |
| 41. C22×ΓL(1,𝔽8) | C4⋊C4 | semidirect |
| 48. ΓL(1,𝔽8)⋊C4 | C22×C4 | semidirect |
| 57. C2×Dic7 | C2×C3×C4 | semidirect |
| 68. C2×ΓL(1,𝔽8) | C2×C4⋊C4 | semidirect |
| 76. C22×C7 | C3×C4⋊C4 | semidirect |
| 83. Dic7 | C22×C3×C4 | semidirect |
| 94. ΓL(1,𝔽8) | C22×C4⋊C4 | semidirect |
| 103. C2×C7 | C2×C3×C4⋊C4 | semidirect |
| 125. C7 | C22×C3×C4⋊C4 | semidirect |
| 130. C22 | (ΓL(1,𝔽8)⋊C4)⋊C4 | direct (N × H) |
| 139. C2 | C2×(ΓL(1,𝔽8)⋊C4)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×ΓL(1,𝔽8) | 2 |
| C23×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×(ΓL(1,𝔽8)⋊C4)⋊C4 | 2 |
| C22×Dic7⋊C4 | 3 |
| C22×C3×C4⋊C4 | 7 |