Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 164 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 |
|---|---|---|
| 2. #10623904 | C2 | semidirect |
| 3. C5×#3748 | C2 | semidirect |
| 4. #10623754 | C2 | semidirect |
| 5. D5×C3⋊(C3⋊C8) | C2 | semidirect |
| 14. C3⋊(C3⋊#168) | C22 | semidirect |
| 15. C5×C3⋊(C3⋊C8) | C22 | semidirect |
| 34. #3748 | D5 | direct (N × H) |
| 49. C32×D5 | M16 | semidirect |
| 63. C3⋊(C3⋊C8) | C2×D5 | semidirect |
| 77. C32×C5 | C2×M16 | semidirect |
| 99. C3×D5 | #208 | semidirect |
| 126. C3×C5 | C2×#208 | semidirect |
| 138. D5 | #3748 | direct (N × H) |
| 139. C32 | D5×M16 | semidirect |
| 153. C5 | C2×#3748 | semidirect |
| 162. C3 | D5×#208 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D5 | 2 |
| #10623904 | 2 |
| C5×#3748 | 2 |
| #10623754 | 2 |
| D5×C3⋊(C3⋊C8) | 2 |
| D5×#208 | 3 |
| C2×#3748 | 5 |