Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 1. C5×#3832 | C2 | semidirect |
| 2. #10624220 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×#6717 | C2 | semidirect |
| 5. #10623824 | C2 | semidirect |
| 6. #10623821 | C2 | semidirect |
| 7. #10623818 | C2 | semidirect |
| 27. #6718 | D3 | semidirect |
| 28. #6717 | D3 | semidirect |
| 45. #3832 | D5 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #916 | semidirect |
| 215. C3×C5 | #919 | semidirect |
| 239. C32 | #4096 | semidirect |
| 262. C5 | #63950 | semidirect |
| 271. C3 | #91517 | semidirect |
| 272. C3 | #91519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3832 | 2 |
| #10624220 | 2 |
| C3×#6718 | 2 |
| C3×#6717 | 2 |
| #10623824 | 2 |
| #10623821 | 2 |
| #10623818 | 2 |
| #91519 | 3 |
| #91517 | 3 |
| #63950 | 5 |