Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
280 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10624222 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. #10623824 | C2 | semidirect |
| 5. #10623820 | C2 | semidirect |
| 20. #6718 | D3 | semidirect |
| 91. C32×C5 | #137 | semidirect |
| 145. C3×C5 | #918 | semidirect |
| 161. C32 | #4097 | semidirect |
| 177. C5 | #63945 | semidirect |
| 185. C3 | #91510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| #10624222 | 2 |
| C3×#6718 | 2 |
| #10623824 | 2 |
| #10623820 | 2 |
| #91510 | 3 |
| #63945 | 5 |