Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10624283 | C2 | semidirect |
| 2. C2×C32×D20 | C2 | semidirect |
| 3. C5×#3748 | C2 | semidirect |
| 4. #10623762 | C2 | semidirect |
| 5. #10623758 | C2 | semidirect |
| 10. C4⋊(C3⋊D15) | C22 | semidirect |
| 12. #67180 | C22 | semidirect |
| 15. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 18. C2×C3×D20 | D3 | semidirect |
| 34. #3748 | D5 | semidirect |
| 50. C2×D20 | C3⋊D3 | semidirect |
| 62. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 122. C3×C5 | #932 | semidirect |
| 134. C32 | #4054 | semidirect |
| 148. C5 | #64141 | semidirect |
| 156. C3 | #91312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624283 | 2 |
| C2×C32×D20 | 2 |
| C5×#3748 | 2 |
| #10623762 | 2 |
| #10623758 | 2 |
| #91312 | 3 |
| #64141 | 5 |