Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
264 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 1. C3×D4×AGL(1,𝔽5) | C2 | semidirect |
| 3. C3×#4007 | C2 | semidirect |
| 4. C3×#3993 | C2 | semidirect |
| 5. C3×#3992 | C2 | semidirect |
| 6. #65731 | C3 | direct (N × H) |
| 13. C3×C5×D8 | C4 | semidirect |
| 14. C3×#686 | C4 | semidirect |
| 15. C3×D40 | C4 | semidirect |
| 18. D4×AGL(1,𝔽5) | C2×C3 | semidirect |
| 20. #4007 | C2×C3 | semidirect |
| 21. #3993 | C2×C3 | semidirect |
| 22. #3992 | C2×C3 | semidirect |
| 27. C3×C5×D4 | C2×C4 | semidirect |
| 29. C3×D20 | C2×C4 | semidirect |
| 32. C3×C5×C8 | C2×C4 | semidirect |
| 33. C3×#168 | C2×C4 | semidirect |
| 45. C5×D8 | C3×C4 | semidirect |
| 46. #686 | C3×C4 | semidirect |
| 47. D40 | C3×C4 | semidirect |
| 63. C3×D8 | AGL(1,𝔽5) | semidirect |
| 73. C5×D4 | C2×C3×C4 | semidirect |
| 75. D20 | C2×C3×C4 | semidirect |
| 78. C5×C8 | C2×C3×C4 | semidirect |
| 79. #168 | C2×C3×C4 | semidirect |
| 92. C3×D4 | C2×AGL(1,𝔽5) | semidirect |
| 99. C3×C8 | C2×AGL(1,𝔽5) | semidirect |
| 113. D8 | C3×AGL(1,𝔽5) | semidirect |
| 119. C3×C5 | #442 | semidirect |
| 136. D4 | C2×C3×AGL(1,𝔽5) | semidirect |
| 143. C8 | C2×C3×AGL(1,𝔽5) | semidirect |
| 148. C5 | C3×#442 | semidirect |
| 158. C3 | #65731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×AGL(1,𝔽5) | 2 |
| C3×D5×D8 | 2 |
| C3×#4007 | 2 |
| C3×#3993 | 2 |
| C3×#3992 | 2 |
| #65731 | 3 |
| C3×#442 | 5 |