Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 112 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. #6489⋊C3 | C2 | semidirect |
| 3. C2×#1136⋊C3 | C2 | semidirect |
| 4. #6406⋊C3 | C2 | semidirect |
| 5. #89987 | C3 | semidirect |
| 9. C2×D4×ΓL(1,𝔽8) | C4 | semidirect |
| 13. C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | semidirect |
| 16. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 18. #6489 | C2×C3 | semidirect |
| 19. C2×#1136 | C2×C3 | semidirect |
| 20. #6406 | C2×C3 | semidirect |
| 38. C2×C7×D4 | C3×C4 | semidirect |
| 42. C4⋊Dic7 | C22×C3 | semidirect |
| 45. C2×C7⋊C8 | C22×C3 | semidirect |
| 116. ΓL(1,𝔽8) | #418 | semidirect |
| 120. C2×D4 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 155. C7 | C3×#418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×ΓL(1,𝔽8) | 2 |
| #6489⋊C3 | 2 |
| C2×#1136⋊C3 | 2 |
| #6406⋊C3 | 2 |
| #89987 | 3 |
| C3×#418 | 7 |