Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
694 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 170 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×#67180 | C2 | semidirect |
| 2. C2×C3×C4×D15 | C2 | semidirect |
| 3. C2×C3×C5×D12 | C2 | semidirect |
| 4. C2×#67150 | C2 | semidirect |
| 5. C2×D3×Dic15 | C2 | semidirect |
| 6. #10624200 | C2 | direct (N × H) |
| 13. #67180 | C22 | semidirect |
| 15. C3×C4×D15 | C22 | semidirect |
| 16. C3×C5×D12 | C22 | semidirect |
| 17. #67150 | C22 | semidirect |
| 18. D3×Dic15 | C22 | semidirect |
| 24. C2×C4×D15 | D3 | semidirect |
| 28. C2×C5×D12 | D3 | semidirect |
| 43. C2×C3×D12 | D5 | semidirect |
| 62. C4×D15 | C2×D3 | semidirect |
| 66. C5×D12 | C2×D3 | semidirect |
| 73. C2×C32×C5 | #41 | semidirect |
| 89. C3×D12 | C2×D5 | semidirect |
| 119. C2×D12 | D15 | semidirect |
| 125. C32×C5 | C2×#41 | semidirect |
| 148. C2×C3×C5 | #235 | semidirect |
| 149. C2×C3×C5 | #237 | semidirect |
| 172. D12 | C2×D15 | semidirect |
| 186. C2×C32 | #711 | semidirect |
| 197. C3×C5 | C2×#235 | semidirect |
| 198. C3×C5 | C2×#237 | semidirect |
| 219. C2×C5 | #3795 | semidirect |
| 222. C32 | C2×#711 | semidirect |
| 237. C2×C3 | #6772 | semidirect |
| 238. C2×C3 | #6819 | semidirect |
| 243. C5 | C2×#3795 | semidirect |
| 253. C3 | C2×#6772 | semidirect |
| 254. C3 | C2×#6819 | semidirect |
| 257. C2 | #10624200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67180 | 2 |
| C2×C3×C4×D15 | 2 |
| C2×C3×C5×D12 | 2 |
| C2×#67150 | 2 |
| C2×D3×Dic15 | 2 |
| #10624200 | 2 |
| C2×#6819 | 3 |
| C2×#6772 | 3 |
| C2×#3795 | 5 |