Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 135 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. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 4. C7×#423 | C3 | semidirect |
| 14. C7×C4⋊C8 | C2×C3 | semidirect |
| 40. C4×ΓL(1,𝔽8) | M16 | semidirect |
| 43. #423 | ΓL(1,𝔽8) | direct (N × H) |
| 65. C4⋊C8 | C2×ΓL(1,𝔽8) | semidirect |
| 71. C4×C7 | C3×M16 | semidirect |
| 83. ΓL(1,𝔽8) | #423 | direct (N × H) |
| 111. C7 | C3×#423 | semidirect |
| 120. C4 | M16×ΓL(1,𝔽8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×ΓL(1,𝔽8) | 2 |
| C2×C42×ΓL(1,𝔽8) | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| C7×#423 | 3 |
| C3×#423 | 7 |