Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
358 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C3×D60 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623821 | C2 | direct (N × H) |
| 11. C5×C4⋊(C3⋊D3) | C22 | semidirect |
| 13. C3×D60 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 16. C2×D60 | D3 | semidirect |
| 21. C2×C3⋊#168 | D3 | semidirect |
| 33. C2×C4⋊(C3⋊D3) | D5 | semidirect |
| 46. D60 | C2×D3 | semidirect |
| 55. C3⋊#168 | C2×D3 | semidirect |
| 59. C2×C32×C5 | D8 | semidirect |
| 71. C4⋊(C3⋊D3) | C2×D5 | semidirect |
| 103. C32×C5 | C2×D8 | semidirect |
| 122. C2×C3×C5 | D24 | semidirect |
| 123. C2×C3×C5 | #213 | semidirect |
| 158. C2×C32 | #686 | semidirect |
| 167. C3×C5 | C2×D24 | semidirect |
| 168. C3×C5 | C2×#213 | semidirect |
| 189. C2×C5 | #3714 | semidirect |
| 192. C32 | C2×#686 | semidirect |
| 204. C2×C3 | #6652 | semidirect |
| 205. C2×C3 | #6654 | semidirect |
| 212. C5 | C2×#3714 | semidirect |
| 221. C3 | C2×#6652 | semidirect |
| 222. C3 | C2×#6654 | semidirect |
| 225. C2 | #10623821 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C3×D60 | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623821 | 2 |
| C2×#6654 | 3 |
| C2×#6652 | 3 |
| C2×#3714 | 5 |