Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
284 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 152 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. #6389⋊C3 | C2 | semidirect |
| 5. C8×ΓL(1,𝔽8)⋊C4 | C2 | semidirect |
| 6. M16×Dic7 | C3 | semidirect |
| 9. M16×ΓL(1,𝔽8) | C4 | semidirect |
| 14. #1136⋊C3 | C4 | semidirect |
| 19. #6389 | C2×C3 | semidirect |
| 20. C8×Dic7 | C2×C3 | semidirect |
| 30. C8×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 31. ΓL(1,𝔽8)⋊C8 | C2×C4 | semidirect |
| 34. C7×M16 | C3×C4 | semidirect |
| 39. #1136 | C3×C4 | semidirect |
| 53. ΓL(1,𝔽8)⋊C4 | M16 | direct (N × H) |
| 63. C7×C8 | C2×C3×C4 | semidirect |
| 64. C7⋊C8 | C2×C3×C4 | semidirect |
| 89. Dic7 | C3×M16 | semidirect |
| 100. ΓL(1,𝔽8) | C4×M16 | semidirect |
| 104. M16 | ΓL(1,𝔽8)⋊C4 | direct (N × H) |
| 130. C8 | C2×ΓL(1,𝔽8)⋊C4 | semidirect |
| 131. C7 | C3×C4×M16 | 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 |
| #6389⋊C3 | 2 |
| C8×ΓL(1,𝔽8)⋊C4 | 2 |
| M16×Dic7 | 3 |
| C3×C4×M16 | 7 |