Finite Group DatabasebetaFinite Group DatabasebetaOrder 720.
164 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 72 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×Dic30 | C2 | semidirect |
| 3. C32×Dic10 | C2 | semidirect |
| 4. C3×#1204 | C2 | semidirect |
| 7. D3×Dic10 | C3 | direct (N × H) |
| 15. Dic30 | C2×C3 | semidirect |
| 21. C3×Dic10 | D3 | direct (N × H) |
| 22. C3×Dic10 | C2×C3 | semidirect |
| 23. #1204 | C2×C3 | semidirect |
| 26. C3×C5×D3 | Q8 | semidirect |
| 47. C32×C5 | C2×Q8 | semidirect |
| 52. Dic10 | C3×D3 | direct (N × H) |
| 62. C5×D3 | C3×Q8 | semidirect |
| 80. C3×D3 | Dic10 | direct (N × H) |
| 83. C3×C5 | D3×Q8 | semidirect |
| 84. C3×C5 | C2×C3×Q8 | semidirect |
| 99. C32 | C2×Dic10 | semidirect |
| 109. D3 | C3×Dic10 | direct (N × H) |
| 110. C5 | C3×D3×Q8 | semidirect |
| 117. C3 | D3×Dic10 | direct (N × H) |
| 118. C3 | C2×C3×Dic10 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Dic30 | 2 |
| C3×C4×C5×D3 | 2 |
| C32×Dic10 | 2 |
| C3×#1204 | 2 |
| C3×D3×Dic5 | 2 |
| C2×C3×Dic10 | 3 |
| D3×Dic10 | 3 |
| C3×D3×Q8 | 5 |