Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
596 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 192 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. C22×C5×Dic6 | C2 | semidirect |
| 3. C22×C3⋊#168 | C2 | semidirect |
| 4. C2×#6655 | C2 | direct (N × H) |
| 10. C2×C5×Dic6 | C22 | semidirect |
| 13. C2×C3⋊#168 | C22 | semidirect |
| 14. #6655 | C22 | direct (N × H) |
| 27. C5×Dic6 | C23 | semidirect |
| 30. C3⋊#168 | C23 | semidirect |
| 32. C22×Dic6 | D5 | semidirect |
| 45. C22×C3×C5 | SD16 | semidirect |
| 58. C2×Dic6 | C2×D5 | semidirect |
| 76. C2×C3×C5 | C2×SD16 | semidirect |
| 88. Dic6 | C22×D5 | semidirect |
| 90. C22×C5 | #214 | semidirect |
| 106. C3×C5 | C22×SD16 | semidirect |
| 109. C22×C3 | #688 | semidirect |
| 114. C2×C5 | C2×#214 | semidirect |
| 129. C2×C3 | C2×#688 | semidirect |
| 131. C5 | C22×#214 | semidirect |
| 134. C22 | #6655 | direct (N × H) |
| 139. C3 | C22×#688 | semidirect |
| 141. C2 | C2×#6655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic6 | 2 |
| C22×C3×D20 | 2 |
| C22×C3⋊#168 | 2 |
| C2×#6655 | 2 |
| C22×#688 | 3 |
| C22×#214 | 5 |