Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
272 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10587931⋊C3 | C2 | semidirect |
| 3. ΓL(1,𝔽8)×#700 | C2 | semidirect |
| 4. #10587922⋊C3 | C2 | semidirect |
| 5. #170×AGL(1,𝔽7) | C2 | semidirect |
| 6. D7×#700 | C3 | semidirect |
| 14. ΓL(1,𝔽8)⋊#170 | C22 | semidirect |
| 15. ΓL(1,𝔽8)×#170 | C22 | semidirect |
| 18. #10587931 | C2×C3 | semidirect |
| 19. C7×#700 | C2×C3 | semidirect |
| 20. #10587922 | C2×C3 | semidirect |
| 21. D7×#170 | C2×C3 | semidirect |
| 43. C7⋊#170 | C22×C3 | semidirect |
| 44. C7×#170 | C22×C3 | semidirect |
| 54. C5×AGL(1,𝔽7) | M16 | semidirect |
| 87. C5×ΓL(1,𝔽8) | C2×M16 | semidirect |
| 101. #700 | AGL(1,𝔽7) | direct (N × H) |
| 104. C5×D7 | C3×M16 | semidirect |
| 131. AGL(1,𝔽7) | #700 | direct (N × H) |
| 140. #170 | C2×AGL(1,𝔽7) | semidirect |
| 141. C5×C7 | C2×C3×M16 | semidirect |
| 164. ΓL(1,𝔽8) | C2×#700 | semidirect |
| 182. D7 | C3×#700 | semidirect |
| 204. C7 | C2×C3×#700 | semidirect |
| 209. C5 | M16×AGL(1,𝔽7) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D5×AGL(1,𝔽7) | 2 |
| #10587931⋊C3 | 2 |
| ΓL(1,𝔽8)×#700 | 2 |
| #10587922⋊C3 | 2 |
| #170×AGL(1,𝔽7) | 2 |
| D7×#700 | 3 |
| M16×AGL(1,𝔽7) | 5 |
| C2×C3×#700 | 7 |