Finite Group DatabasebetaFinite Group Databasebeta← C2×(ΓL(1,𝔽8)⋊C4)⋊C8 #13051999
Order 1344.
276 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 144 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. (ΓL(1,𝔽8)⋊C4)⋊C8 | C2 | direct (N × H) |
| 5. C2×Dic7⋊C8 | C3 | semidirect |
| 18. Dic7⋊C8 | C2×C3 | semidirect |
| 26. C2×ΓL(1,𝔽8)⋊C4 | C8 | semidirect |
| 52. ΓL(1,𝔽8)⋊C4 | C2×C8 | semidirect |
| 60. C2×Dic7 | C3×C8 | semidirect |
| 74. C2×ΓL(1,𝔽8) | C4⋊C8 | semidirect |
| 90. Dic7 | C2×C3×C8 | semidirect |
| 102. ΓL(1,𝔽8) | C2×C4⋊C8 | semidirect |
| 112. C2×C7 | C3×C4⋊C8 | semidirect |
| 136. C7 | C2×C3×C4⋊C8 | semidirect |
| 151. C2 | (ΓL(1,𝔽8)⋊C4)⋊C8 | direct (N × H) |
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×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| C22×ΓL(1,𝔽8)⋊C8 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| C2×Dic7⋊C8 | 3 |
| C2×C3×C4⋊C8 | 7 |