Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
134 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 46 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 |
|---|---|---|
| 2. C5×Q8×Dic3 | C3 | semidirect |
| 5. C3×C5×SL(2,𝔽3) | C4 | semidirect |
| 6. Dic3×SL(2,𝔽3) | C5 | direct (N × H) |
| 17. C3×C5×Q8 | C3×C4 | semidirect |
| 23. C5×SL(2,𝔽3) | Dic3 | direct (N × H) |
| 24. Q8×Dic3 | C3×C5 | semidirect |
| 33. C3×SL(2,𝔽3) | C4×C5 | semidirect |
| 41. C5×Dic3 | SL(2,𝔽3) | direct (N × H) |
| 49. C5×Q8 | C3×Dic3 | semidirect |
| 66. C3×Q8 | C3×C4×C5 | semidirect |
| 72. SL(2,𝔽3) | C5×Dic3 | direct (N × H) |
| 86. C3×C5 | C4×SL(2,𝔽3) | semidirect |
| 94. Dic3 | C5×SL(2,𝔽3) | direct (N × H) |
| 100. Q8 | C3×C5×Dic3 | semidirect |
| 113. C5 | Dic3×SL(2,𝔽3) | direct (N × H) |
| 121. C3 | C4×C5×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×SL(2,𝔽3) | 2 |
| C5×Q8×Dic3 | 3 |
| C4×C5×SL(2,𝔽3) | 3 |
| C2×C3×C5×Dic3 | 4 |
| Dic3×SL(2,𝔽3) | 5 |