Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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×C5×C4⋊Q8 | C2 | semidirect |
| 2. C2×C3×#688 | C2 | semidirect |
| 4. C3×C4×#168 | C2 | semidirect |
| 5. #65374 | C3 | direct (N × H) |
| 14. C5×C4⋊Q8 | C2×C3 | semidirect |
| 15. C2×#688 | C2×C3 | semidirect |
| 17. C4×#168 | C2×C3 | semidirect |
| 25. C3×#168 | D4 | semidirect |
| 27. C3×C4⋊Q8 | D5 | semidirect |
| 42. C3×C4×C5 | SD16 | semidirect |
| 58. #168 | C3×D4 | semidirect |
| 60. C4⋊Q8 | C3×D5 | semidirect |
| 78. C4×C5 | C3×SD16 | semidirect |
| 87. C3×C5 | #492 | semidirect |
| 92. C3×C4 | #688 | semidirect |
| 108. C5 | C3×#492 | semidirect |
| 113. C4 | C3×#688 | semidirect |
| 115. C3 | #65374 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C2×C3×#688 | 2 |
| C3×#4020 | 2 |
| C3×C4×#168 | 2 |
| #65374 | 3 |
| C3×#492 | 5 |