Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10624285 | C2 | semidirect |
| 2. #10624196 | C2 | semidirect |
| 3. C3×#6716 | C2 | semidirect |
| 4. C3×C5×#213 | C2 | semidirect |
| 5. #10623808 | C2 | semidirect |
| 6. #10623805 | C2 | semidirect |
| 7. #10623794 | C2 | semidirect |
| 29. #6716 | D3 | semidirect |
| 32. C5×#213 | D3 | semidirect |
| 48. C3×#213 | D5 | semidirect |
| 132. #213 | D15 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #912 | semidirect |
| 215. C3×C5 | #916 | semidirect |
| 239. C32 | #4058 | semidirect |
| 262. C5 | #63936 | semidirect |
| 271. C3 | #91499 | semidirect |
| 272. C3 | #91801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624285 | 2 |
| #10624196 | 2 |
| C3×#6716 | 2 |
| C3×C5×#213 | 2 |
| #10623808 | 2 |
| #10623805 | 2 |
| #10623794 | 2 |
| #91801 | 3 |
| #91499 | 3 |
| #63936 | 5 |