Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
140 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 39 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. C7×#354 | C3 | semidirect |
| 4. C2×Q8×ΓL(1,𝔽8) | C4 | semidirect |
| 8. C42×ΓL(1,𝔽8) | C4 | semidirect |
| 19. C2×C7×Q8 | C3×C4 | semidirect |
| 23. C42×C7 | C3×C4 | semidirect |
| 33. #354 | ΓL(1,𝔽8) | direct (N × H) |
| 65. ΓL(1,𝔽8) | #354 | direct (N × H) |
| 66. C2×Q8 | C4×ΓL(1,𝔽8) | semidirect |
| 70. C42 | C4×ΓL(1,𝔽8) | semidirect |
| 88. C7 | C3×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#124 | 2 |
| ΓL(1,𝔽8)×#99 | 2 |
| C7×#354 | 3 |
| C3×#354 | 7 |