Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 104 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. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 3. C2×#1136⋊C3 | C2 | semidirect |
| 4. #6383⋊C3 | C2 | semidirect |
| 5. #89773 | C3 | semidirect |
| 10. C2×C4⋊AGL(1,𝔽7) | C4 | semidirect |
| 12. C4⋊C4×ΓL(1,𝔽8) | C22 | semidirect |
| 16. C2×ΓL(1,𝔽8)⋊C8 | C22 | semidirect |
| 18. C7×#117 | C2×C3 | semidirect |
| 19. C2×#1136 | C2×C3 | semidirect |
| 20. #6383 | C2×C3 | semidirect |
| 39. C2×D28 | C3×C4 | semidirect |
| 41. C7×C4⋊C4 | C22×C3 | semidirect |
| 45. C2×C7⋊C8 | C22×C3 | semidirect |
| 91. #117 | AGL(1,𝔽7) | semidirect |
| 116. ΓL(1,𝔽8) | #418 | semidirect |
| 125. C4⋊C4 | C2×AGL(1,𝔽7) | 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×C4⋊AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×#117 | 2 |
| C2×#1136⋊C3 | 2 |
| #6383⋊C3 | 2 |
| #89773 | 3 |
| C3×#418 | 7 |