Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. C2×C32×C5×D4 | C2 | semidirect |
| 2. #10624283 | C2 | semidirect |
| 3. #10623910 | C2 | semidirect |
| 4. #10623909 | C2 | semidirect |
| 5. #10623904 | C2 | semidirect |
| 12. C4⋊(C3⋊D15) | C22 | semidirect |
| 14. #67180 | C22 | semidirect |
| 15. C3⋊(C3⋊#168) | C22 | semidirect |
| 17. C2×C3×C5×D4 | D3 | semidirect |
| 30. C2×C32×D4 | D5 | semidirect |
| 49. C2×C5×D4 | C3⋊D3 | semidirect |
| 70. C2×C3×D4 | D15 | semidirect |
| 75. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 118. C2×D4 | C3⋊D15 | semidirect |
| 122. C3×C5 | #932 | semidirect |
| 134. C32 | #4078 | semidirect |
| 148. C5 | #64141 | semidirect |
| 156. C3 | #91821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×D4 | 2 |
| #10624283 | 2 |
| #10623910 | 2 |
| #10623909 | 2 |
| #10623904 | 2 |
| #91821 | 3 |
| #64141 | 5 |