Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
124 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 44. C3×C4×C5 | C32 | semidirect |
| 74. C4×C5 | C3⋊C32 | semidirect |
| 83. C3×C5 | C4⋊C32 | semidirect |
| 86. C3×C4 | #3928 | semidirect |
| 101. C5 | C4⋊(C3⋊C32) | semidirect |
| 104. C4 | C3⋊#3928 | semidirect |
| 107. C3 | C4⋊#3928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊#3928 | 2 |
| C3×C4×#672 | 2 |
| C4⋊#3928 | 3 |
| C4⋊(C3⋊C32) | 5 |