Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
302 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 27. C32×C4×C5 | Q8 | semidirect |
| 29. C3⋊Dic15 | Q8 | semidirect |
| 74. C3×C4×C5 | Dic6 | semidirect |
| 75. C3×C4×C5 | Dic6 | semidirect |
| 96. C32×C5 | C4⋊Q8 | semidirect |
| 104. C32×C4 | Dic10 | semidirect |
| 136. C4×C5 | #627 | semidirect |
| 149. C3×C5 | #888 | semidirect |
| 150. C3×C5 | #888 | semidirect |
| 157. C3×C4 | #1204 | semidirect |
| 158. C3×C4 | Dic30 | semidirect |
| 170. C32 | #4034 | semidirect |
| 186. C5 | #63919 | semidirect |
| 192. C4 | #67153 | semidirect |
| 194. C3 | #91470 | semidirect |
| 195. C3 | #91777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67153 | 2 |
| C4×C3⋊Dic15 | 2 |
| C3×C4⋊Dic15 | 2 |
| C3×C5×C4⋊Dic3 | 2 |
| #10623815 | 2 |
| #91777 | 3 |
| #91470 | 3 |
| #63919 | 5 |