Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
112 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 42 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 |
|---|---|---|
| 2. #6393⋊C3 | C2 | semidirect |
| 3. C2×ΓL(1,𝔽8)⋊C16 | C2 | semidirect |
| 4. #89362 | C3 | semidirect |
| 13. #6393 | C2×C3 | semidirect |
| 14. C2×C7⋊C16 | C2×C3 | semidirect |
| 74. ΓL(1,𝔽8) | #359 | semidirect |
| 98. C7 | C3×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#135 | 2 |
| #6393⋊C3 | 2 |
| C2×ΓL(1,𝔽8)⋊C16 | 2 |
| #89362 | 3 |
| C3×#359 | 7 |