Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
384 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 128 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×#65702 | C2 | semidirect |
| 3. C3×#64881 | C2 | semidirect |
| 4. C3×#64879 | C2 | semidirect |
| 5. C3×#64871 | C2 | semidirect |
| 6. #10604062 | C3 | direct (N × H) |
| 18. #65702 | C2×C3 | semidirect |
| 20. #64881 | C2×C3 | semidirect |
| 21. #64879 | C2×C3 | semidirect |
| 22. #64871 | C2×C3 | semidirect |
| 34. C3×D40 | C8 | semidirect |
| 57. C3×D20 | C2×C8 | semidirect |
| 63. C3×C5×C8 | C2×C8 | semidirect |
| 86. D40 | C3×C8 | semidirect |
| 119. D20 | C2×C3×C8 | semidirect |
| 125. C5×C8 | C2×C3×C8 | semidirect |
| 154. C3×C8 | D5⋊C8 | semidirect |
| 176. C3×C5 | #1580 | semidirect |
| 203. C8 | C3×D5⋊C8 | semidirect |
| 208. C5 | C3×#1580 | semidirect |
| 218. C3 | #10604062 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#65702 | 2 |
| C3×#65161 | 2 |
| C3×#64881 | 2 |
| C3×#64879 | 2 |
| C3×#64871 | 2 |
| #10604062 | 3 |
| C3×#1580 | 5 |