Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
296 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 2. C2×Q16×ΓL(1,𝔽8) | C2 | semidirect |
| 4. C2×#1144⋊C3 | C2 | semidirect |
| 5. #6409⋊C3 | C2 | semidirect |
| 7. #6390⋊C3 | C2 | semidirect |
| 8. #89958 | C3 | semidirect |
| 25. C2×C7×Q16 | C2×C3 | semidirect |
| 27. C2×#1144 | C2×C3 | semidirect |
| 28. #6409 | C2×C3 | semidirect |
| 30. #6390 | C2×C3 | semidirect |
| 76. C2×AGL(1,𝔽7) | Q16 | semidirect |
| 125. C2×Q16 | AGL(1,𝔽7) | semidirect |
| 133. C2×D7 | C3×Q16 | semidirect |
| 160. ΓL(1,𝔽8) | #451 | semidirect |
| 210. C7 | C3×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×AGL(1,𝔽7) | 2 |
| C2×Q16×ΓL(1,𝔽8) | 2 |
| #6509⋊C3 | 2 |
| C2×#1144⋊C3 | 2 |
| #6409⋊C3 | 2 |
| (C2×AGL(1,𝔽7))⋊C8 | 2 |
| #6390⋊C3 | 2 |
| #89958 | 3 |
| C3×#451 | 7 |