Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 46 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. C4×C7⋊SL(2,𝔽3) | C2 | semidirect |
| 3. C7×#520 | C3 | semidirect |
| 4. #41⋊ΓL(1,𝔽8) | C4 | semidirect |
| 13. C7⋊SL(2,𝔽3) | C2×C4 | semidirect |
| 17. C7×#41 | C3×C4 | semidirect |
| 32. #520 | ΓL(1,𝔽8) | semidirect |
| 70. #41 | C4×ΓL(1,𝔽8) | semidirect |
| 99. C7 | #520⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊ΓL(1,𝔽8) | 2 |
| C4×C7⋊SL(2,𝔽3) | 2 |
| C7×#520 | 3 |
| C4⋊C4×ΓL(1,𝔽8) | 4 |
| #520⋊C3 | 7 |