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. #10624287 | C2 | semidirect |
| 2. #10624196 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623804 | C2 | semidirect |
| 6. #10623800 | C2 | semidirect |
| 7. #10623794 | C2 | semidirect |
| 28. #6718 | D3 | semidirect |
| 32. C5×#215 | D3 | semidirect |
| 48. C3×#215 | D5 | semidirect |
| 131. #215 | D15 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #916 | semidirect |
| 215. C3×C5 | #919 | semidirect |
| 239. C32 | #4062 | semidirect |
| 262. C5 | #63950 | semidirect |
| 271. C3 | #91523 | semidirect |
| 272. C3 | #91805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624287 | 2 |
| #10624196 | 2 |
| C3×#6718 | 2 |
| C3×C5×#215 | 2 |
| #10623804 | 2 |
| #10623800 | 2 |
| #10623794 | 2 |
| #91805 | 3 |
| #91523 | 3 |
| #63950 | 5 |