Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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×#1132⋊C3 | C2 | semidirect |
| 3. #6438⋊C3 | C2 | semidirect |
| 4. C4×C4⋊AGL(1,𝔽7) | C2 | semidirect |
| 5. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 6. #6395⋊C3 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89616 | C3 | semidirect |
| 23. C2×#1132 | C2×C3 | semidirect |
| 24. #6438 | C2×C3 | semidirect |
| 25. C4×D28 | C2×C3 | semidirect |
| 26. C7×C4⋊C8 | C2×C3 | semidirect |
| 27. #6395 | C2×C3 | semidirect |
| 28. #6390 | C2×C3 | semidirect |
| 118. C4⋊C8 | AGL(1,𝔽7) | semidirect |
| 150. ΓL(1,𝔽8) | #463 | semidirect |
| 198. C7 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D56⋊C3 | 2 |
| C2×#1132⋊C3 | 2 |
| #6438⋊C3 | 2 |
| C4×C4⋊AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| #6395⋊C3 | 2 |
| #6390⋊C3 | 2 |
| #89616 | 3 |
| C3×#463 | 7 |