Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
338 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 86 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. Dic3⋊ΓL(1,𝔽16) | C2 | semidirect |
| 5. Dic3×ΓL(1,𝔽16) | C2 | semidirect |
| 11. C2×C3×Dic15 | C4 | semidirect |
| 12. C2×C3×C5×Dic3 | C4 | semidirect |
| 13. C3×D5×Dic3 | C4 | semidirect |
| 14. C3×D5×Dic3 | C4 | semidirect |
| 54. C2×Dic15 | Dic3 | semidirect |
| 55. C2×C5×Dic3 | Dic3 | semidirect |
| 61. D5×Dic3 | Dic3 | semidirect |
| 62. D5×Dic3 | Dic3 | semidirect |
| 84. C2×C3×Dic3 | AGL(1,𝔽5) | semidirect |
| 121. C32×C5 | #117 | semidirect |
| 173. C2×Dic3 | ΓL(1,𝔽16) | semidirect |
| 194. C3×C5 | #877 | semidirect |
| 195. C3×C5 | #926 | semidirect |
| 225. C32 | #4130 | semidirect |
| 247. C5 | #63955 | semidirect |
| 259. C3 | #91923 | semidirect |
| 260. C3 | #91989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D5×Dic3 | 2 |
| #10624098 | 2 |
| C3×#6763 | 2 |
| Dic3⋊ΓL(1,𝔽16) | 2 |
| Dic3×ΓL(1,𝔽16) | 2 |
| #91989 | 3 |
| #91923 | 3 |
| #63955 | 5 |