Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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. #10624097 | C2 | semidirect |
| 3. C3×#6762 | C2 | semidirect |
| 4. #10623976 | C2 | semidirect |
| 5. #10623974 | C2 | semidirect |
| 15. C3⋊(C3⋊#170) | C22 | semidirect |
| 16. C3×C3⋊#170 | C22 | semidirect |
| 23. #6762 | D3 | semidirect |
| 61. C3⋊#170 | C2×D3 | semidirect |
| 68. C3×D15 | M16 | semidirect |
| 113. C32×C5 | C2×M16 | semidirect |
| 139. D15 | #208 | semidirect |
| 180. C3×C5 | D3×M16 | semidirect |
| 181. C3×C5 | C2×#208 | semidirect |
| 205. C32 | D5⋊M16 | semidirect |
| 225. C5 | D3×#208 | semidirect |
| 235. C3 | #91931 | semidirect |
| 236. C3 | D5⋊#208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1200 | 2 |
| #10624097 | 2 |
| C3×#6762 | 2 |
| #10623976 | 2 |
| #10623974 | 2 |
| D5⋊#208 | 3 |
| #91931 | 3 |
| D3×#208 | 5 |