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. #10624194 | C2 | semidirect |
| 3. C3×#6717 | C2 | semidirect |
| 4. C3×C5×#216 | C2 | semidirect |
| 5. #10623806 | C2 | semidirect |
| 6. #10623799 | C2 | semidirect |
| 7. #10623794 | C2 | semidirect |
| 29. #6717 | D3 | semidirect |
| 32. C5×#216 | D3 | semidirect |
| 47. C3×#216 | D5 | semidirect |
| 129. #216 | D15 | semidirect |
| 137. C32×C5 | #135 | semidirect |
| 214. C3×C5 | #916 | semidirect |
| 215. C3×C5 | #919 | semidirect |
| 239. C32 | #4065 | semidirect |
| 262. C5 | #63950 | semidirect |
| 271. C3 | #91521 | semidirect |
| 272. C3 | #91808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624287 | 2 |
| #10624194 | 2 |
| C3×#6717 | 2 |
| C3×C5×#216 | 2 |
| #10623806 | 2 |
| #10623799 | 2 |
| #10623794 | 2 |
| #91808 | 3 |
| #91521 | 3 |
| #63950 | 5 |