Finite Group DatabasebetaFinite Group DatabasebetaOrder 2016.
292 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 96 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. C3×M16×ΓL(1,𝔽8) | C2 | semidirect |
| 3. #66627⋊C3 | C2 | semidirect |
| 4. #66622⋊C3 | C2 | semidirect |
| 5. C8×C3⋊AGL(1,𝔽7) | C2 | semidirect |
| 6. M16×D21 | C3 | semidirect |
| 15. C3×C8×ΓL(1,𝔽8) | C22 | semidirect |
| 16. C3⋊(ΓL(1,𝔽8)⋊C8) | C22 | semidirect |
| 19. C3×C7×M16 | C2×C3 | semidirect |
| 20. #66627 | C2×C3 | semidirect |
| 21. #66622 | C2×C3 | semidirect |
| 22. C8×D21 | C2×C3 | semidirect |
| 24. M16×ΓL(1,𝔽8) | D3 | semidirect |
| 53. C3×C7×C8 | C22×C3 | semidirect |
| 54. C3⋊(C7⋊C8) | C22×C3 | semidirect |
| 56. C8×ΓL(1,𝔽8) | C2×D3 | semidirect |
| 66. C3⋊AGL(1,𝔽7) | M16 | direct (N × H) |
| 68. C7×M16 | C3×D3 | semidirect |
| 102. C3×ΓL(1,𝔽8) | C2×M16 | semidirect |
| 110. C7×C8 | C2×C3×D3 | semidirect |
| 118. C3×M16 | AGL(1,𝔽7) | semidirect |
| 126. D21 | C3×M16 | semidirect |
| 168. C3×C8 | C2×AGL(1,𝔽7) | semidirect |
| 170. C3×C7 | C2×C3×M16 | semidirect |
| 172. ΓL(1,𝔽8) | D3×M16 | semidirect |
| 180. M16 | C3⋊AGL(1,𝔽7) | direct (N × H) |
| 214. C8 | C2×C3⋊AGL(1,𝔽7) | semidirect |
| 215. C7 | C3×D3×M16 | semidirect |
| 236. C3 | M16×AGL(1,𝔽7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊AGL(1,𝔽7) | 2 |
| C3×M16×ΓL(1,𝔽8) | 2 |
| #66627⋊C3 | 2 |
| #66622⋊C3 | 2 |
| C8×C3⋊AGL(1,𝔽7) | 2 |
| M16×D21 | 3 |
| M16×AGL(1,𝔽7) | 3 |
| C3×D3×M16 | 7 |