Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 112 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 | semidirect |
| 5. #89890 | C3 | semidirect |
| 18. Dic7⋊C8 | C2×C3 | semidirect |
| 50. ΓL(1,𝔽8)⋊C4 | M16 | semidirect |
| 85. Dic7 | C3×M16 | semidirect |
| 96. ΓL(1,𝔽8) | #423 | semidirect |
| 127. C7 | C3×#423 | 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×C4×ΓL(1,𝔽8)⋊C4 | 2 |
| C2×#1136⋊C3 | 2 |
| (ΓL(1,𝔽8)⋊C4)⋊C8 | 2 |
| #89890 | 3 |
| C3×#423 | 7 |