Finite Group DatabasebetaFinite Group DatabasebetaOrder 3360.
304 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. C4⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)) | C2 | semidirect |
| 4. C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5) | C2 | semidirect |
| 5. #11765360 | C3 | semidirect |
| 8. C2×C4×C5×ΓL(1,𝔽8) | C4 | semidirect |
| 9. C2×Dic5×ΓL(1,𝔽8) | C4 | semidirect |
| 10. C4×D5×ΓL(1,𝔽8) | C4 | semidirect |
| 11. C4×D5×ΓL(1,𝔽8) | C4 | semidirect |
| 17. C4⋊(C7⋊AGL(1,𝔽5)) | C2×C3 | semidirect |
| 18. C4×C7⋊AGL(1,𝔽5) | C2×C3 | semidirect |
| 35. C2×C4×C5×C7 | C3×C4 | semidirect |
| 36. C2×C7×Dic5 | C3×C4 | semidirect |
| 37. C4×C7×D5 | C3×C4 | semidirect |
| 38. C4×C7×D5 | C3×C4 | semidirect |
| 56. C2×C4×ΓL(1,𝔽8) | AGL(1,𝔽5) | semidirect |
| 80. C5×ΓL(1,𝔽8) | #117 | semidirect |
| 114. C2×C4×C7 | C3×AGL(1,𝔽5) | semidirect |
| 126. C2×C4×C5 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 127. C2×Dic5 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 128. C4×D5 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 129. C4×D5 | ΓL(1,𝔽8)⋊C4 | semidirect |
| 132. C5×C7 | C3×#117 | semidirect |
| 155. ΓL(1,𝔽8) | #4130 | semidirect |
| 194. C2×C4 | ΓL(1,𝔽8)⋊AGL(1,𝔽5) | semidirect |
| 195. C7 | C3×#4130 | semidirect |
| 200. C5 | #6489⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D5×ΓL(1,𝔽8) | 2 |
| (C22⋊(C7⋊AGL(1,𝔽5)))⋊C3 | 2 |
| C4⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽5)) | 2 |
| C4×ΓL(1,𝔽8)⋊AGL(1,𝔽5) | 2 |
| #11765360 | 3 |
| #6489⋊C3 | 5 |
| C3×#4130 | 7 |