Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C4⋊(ΓL(1,𝔽8)⋊C4) | C2 | semidirect |
| 3. #6406⋊C3 | C2 | semidirect |
| 4. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 5. #6381⋊C3 | C2 | semidirect |
| 6. #89805 | C3 | semidirect |
| 17. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 18. #6406 | C2×C3 | semidirect |
| 19. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 20. #6381 | C2×C3 | semidirect |
| 111. ΓL(1,𝔽8) | #480 | semidirect |
| 148. C7 | C3×#480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| ΓL(1,𝔽8)×#121 | 2 |
| C2×C4⋊(ΓL(1,𝔽8)⋊C4) | 2 |
| #6406⋊C3 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| #6381⋊C3 | 2 |
| #89805 | 3 |
| C3×#480 | 7 |