Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
328 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. #10598585 | C3 | direct (N × H) |
| 10. C3×#4002 | C4 | semidirect |
| 12. C3×C5×C4⋊C8 | C4 | semidirect |
| 15. C3×C4⋊#168 | C4 | semidirect |
| 42. #4002 | C3×C4 | semidirect |
| 44. C5×C4⋊C8 | C3×C4 | semidirect |
| 47. C4⋊#168 | C3×C4 | semidirect |
| 72. C3×C4⋊C8 | AGL(1,𝔽5) | semidirect |
| 145. C4⋊C8 | C3×AGL(1,𝔽5) | semidirect |
| 201. C3×C5 | #1285 | semidirect |
| 243. C5 | C3×#1285 | semidirect |
| 257. C3 | #10598585 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C4⋊AGL(1,𝔽5) | 2 |
| C3×#65683 | 2 |
| C3×#65124 | 2 |
| #10598585 | 3 |
| C3×#1285 | 5 |