Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 1. C2×M16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #6487⋊C3 | C2 | semidirect |
| 4. C2×#1132⋊C3 | C2 | semidirect |
| 5. #6395⋊C3 | C2 | semidirect |
| 6. #6392⋊C3 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89906 | C3 | semidirect |
| 22. C2×C7×M16 | C2×C3 | semidirect |
| 24. #6487 | C2×C3 | semidirect |
| 25. C2×#1132 | C2×C3 | semidirect |
| 26. #6395 | C2×C3 | semidirect |
| 27. #6392 | C2×C3 | semidirect |
| 28. #6390 | C2×C3 | semidirect |
| 45. C8×ΓL(1,𝔽8) | D4 | semidirect |
| 95. C7×C8 | C3×D4 | semidirect |
| 115. C2×M16 | AGL(1,𝔽7) | semidirect |
| 150. ΓL(1,𝔽8) | #468 | semidirect |
| 197. C8 | (C22⋊D7)⋊C3 | semidirect |
| 198. C7 | C3×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×ΓL(1,𝔽8) | 2 |
| #6493⋊C3 | 2 |
| #6487⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| #6395⋊C3 | 2 |
| #6392⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89906 | 3 |
| C3×#468 | 7 |