Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 10. C3×#4002 | C4 | semidirect |
| 12. C4⋊(C3⋊#168) | C4 | semidirect |
| 13. C5×C4⋊(C3⋊C8) | C4 | semidirect |
| 42. #4002 | Dic3 | semidirect |
| 75. C4⋊(C3⋊C8) | AGL(1,𝔽5) | semidirect |
| 195. C3×C5 | #1300 | semidirect |
| 233. C5 | #67665 | semidirect |
| 246. C3 | #10598584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752345 | 2 |
| C3×C4×#700 | 2 |
| #11746871 | 2 |
| #10598584 | 3 |
| #67665 | 5 |