Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 76 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. C2×Dic28⋊C3 | C2 | semidirect |
| 4. #6392⋊C3 | C2 | semidirect |
| 5. #6390⋊C3 | C2 | semidirect |
| 6. #89888 | C3 | semidirect |
| 18. C2×Dic28 | C2×C3 | semidirect |
| 19. #6392 | C2×C3 | semidirect |
| 20. #6390 | C2×C3 | semidirect |
| 49. C22×ΓL(1,𝔽8) | Q16 | semidirect |
| 88. C22×C7 | C3×Q16 | semidirect |
| 106. ΓL(1,𝔽8) | #467 | semidirect |
| 140. C7 | C3×#467 | semidirect |
| 147. C22 | Dic28⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×ΓL(1,𝔽8) | 2 |
| #6487⋊C3 | 2 |
| C2×Dic28⋊C3 | 2 |
| #6392⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89888 | 3 |
| C3×#467 | 7 |