Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
408 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×C32×Dic10 | C2 | semidirect |
| 3. C2×C3⋊(C3⋊#168) | C2 | semidirect |
| 4. #10623761 | C2 | direct (N × H) |
| 12. C32×Dic10 | C22 | semidirect |
| 13. C3⋊(C3⋊#168) | C22 | semidirect |
| 16. C2×C3×Dic10 | D3 | semidirect |
| 36. C3×Dic10 | C2×D3 | semidirect |
| 39. C2×C32×C5 | SD16 | semidirect |
| 43. C2×Dic10 | C3⋊D3 | semidirect |
| 64. C32×C5 | C2×SD16 | semidirect |
| 71. Dic10 | C2×C3⋊D3 | semidirect |
| 80. C2×C3×C5 | #215 | semidirect |
| 97. C2×C32 | #687 | semidirect |
| 104. C3×C5 | C2×#215 | semidirect |
| 112. C2×C5 | #3755 | semidirect |
| 114. C32 | C2×#687 | semidirect |
| 123. C2×C3 | #6656 | semidirect |
| 126. C5 | C2×#3755 | semidirect |
| 133. C3 | C2×#6656 | semidirect |
| 135. C2 | #10623761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C2×C32×Dic10 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| #10623761 | 2 |
| C2×#6656 | 3 |
| C2×#3755 | 5 |