Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
460 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 460 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. C2×C3×#4065 | C2 | semidirect |
| 2. C2×C3×#3960 | C2 | semidirect |
| 3. C2×C3×D80 | C2 | semidirect |
| 4. C3×#65172 | C2 | semidirect |
| 5. C3×C5×#358 | C2 | semidirect |
| 6. C3×#64727 | C2 | semidirect |
| 7. C3×#64711 | C2 | semidirect |
| 8. #10600017 | C3 | direct (N × H) |
| 25. C2×#4065 | C2×C3 | semidirect |
| 26. C2×#3960 | C2×C3 | semidirect |
| 27. C2×D80 | C2×C3 | semidirect |
| 28. #65172 | C2×C3 | semidirect |
| 29. C5×#358 | C2×C3 | semidirect |
| 30. #64727 | C2×C3 | semidirect |
| 31. #64711 | C2×C3 | semidirect |
| 42. C3×C5×Q16 | D4 | semidirect |
| 51. C3×D40 | D4 | semidirect |
| 60. C3×#358 | D5 | semidirect |
| 125. C5×Q16 | C3×D4 | semidirect |
| 134. D40 | C3×D4 | semidirect |
| 143. #358 | C3×D5 | semidirect |
| 171. C3×Q16 | D20 | semidirect |
| 273. Q16 | C3×D20 | semidirect |
| 287. C3×C5 | #2186 | semidirect |
| 336. C5 | C3×#2186 | semidirect |
| 352. C3 | #10600017 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#4065 | 2 |
| C2×C3×#3960 | 2 |
| C2×C3×D80 | 2 |
| C3×#65172 | 2 |
| C3×C5×#358 | 2 |
| C3×#64727 | 2 |
| C3×#64711 | 2 |
| #10600017 | 3 |
| C3×#2186 | 5 |