Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 74 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. #6432⋊C3 | C2 | semidirect |
| 4. ΓL(1,𝔽8)×C4⋊C8 | C2 | semidirect |
| 5. #6390⋊C3 | C2 | semidirect |
| 6. #89613 | C3 | semidirect |
| 19. #6432 | C2×C3 | semidirect |
| 20. C7×C4⋊C8 | C2×C3 | semidirect |
| 21. #6390 | C2×C3 | semidirect |
| 55. C4×ΓL(1,𝔽8) | SD16 | semidirect |
| 90. C4⋊C8 | AGL(1,𝔽7) | semidirect |
| 97. C4×C7 | C3×SD16 | semidirect |
| 114. ΓL(1,𝔽8) | #461 | semidirect |
| 151. C7 | C3×#461 | semidirect |
| 163. C4 | #1132⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1132⋊C3 | 2 |
| C4×C4⋊AGL(1,𝔽7) | 2 |
| #6432⋊C3 | 2 |
| ΓL(1,𝔽8)×C4⋊C8 | 2 |
| #6390⋊C3 | 2 |
| #89613 | 3 |
| C3×#461 | 7 |