Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 72 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×SD16×ΓL(1,𝔽8) | C2 | semidirect |
| 2. #6509⋊C3 | C2 | semidirect |
| 4. C2×C8×AGL(1,𝔽7) | C2 | semidirect |
| 5. #6409⋊C3 | C2 | semidirect |
| 6. #6406⋊C3 | C2 | semidirect |
| 7. #6391⋊C3 | C2 | semidirect |
| 8. #89943 | C3 | semidirect |
| 22. C2×C7×SD16 | C2×C3 | semidirect |
| 23. #6509 | C2×C3 | semidirect |
| 25. C2×C8×D7 | C2×C3 | semidirect |
| 26. #6409 | C2×C3 | semidirect |
| 27. #6406 | C2×C3 | semidirect |
| 28. #6391 | C2×C3 | semidirect |
| 44. C8×ΓL(1,𝔽8) | D4 | semidirect |
| 72. C2×AGL(1,𝔽7) | SD16 | semidirect |
| 94. C7×C8 | C3×D4 | semidirect |
| 114. C2×SD16 | AGL(1,𝔽7) | semidirect |
| 127. C2×D7 | C3×SD16 | semidirect |
| 150. ΓL(1,𝔽8) | #465 | semidirect |
| 197. C8 | (C22⋊D7)⋊C3 | semidirect |
| 198. C7 | C3×#465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×ΓL(1,𝔽8) | 2 |
| #6509⋊C3 | 2 |
| #6501⋊C3 | 2 |
| C2×C8×AGL(1,𝔽7) | 2 |
| #6409⋊C3 | 2 |
| #6406⋊C3 | 2 |
| #6391⋊C3 | 2 |
| #89943 | 3 |
| C3×#465 | 7 |