Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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×C3⋊(C3⋊#168) | C2 | semidirect |
| 3. C2×C32×#168 | C2 | semidirect |
| 4. C3⋊D3×#168 | C2 | direct (N × H) |
| 11. C3⋊(C3⋊#168) | C22 | semidirect |
| 12. C32×#168 | C22 | semidirect |
| 16. C2×C3×#168 | D3 | semidirect |
| 19. C2×C5×C3⋊D3 | C8 | semidirect |
| 35. C3×#168 | C2×D3 | semidirect |
| 37. C2×C32×C5 | C2×C8 | semidirect |
| 39. C5×C3⋊D3 | C2×C8 | semidirect |
| 43. C2×#168 | C3⋊D3 | direct (N × H) |
| 61. C32×C5 | C22×C8 | semidirect |
| 68. #168 | C2×C3⋊D3 | direct (N × H) |
| 70. C2×C3⋊D3 | #168 | direct (N × H) |
| 76. C2×C3×C5 | D3×C8 | semidirect |
| 92. C2×C32 | C2×#168 | semidirect |
| 94. C3⋊D3 | C2×#168 | direct (N × H) |
| 99. C3×C5 | C2×D3×C8 | semidirect |
| 107. C2×C5 | C8×C3⋊D3 | semidirect |
| 109. C32 | C22×#168 | semidirect |
| 117. C2×C3 | D3×#168 | semidirect |
| 120. C5 | C2×C8×C3⋊D3 | semidirect |
| 127. C3 | C2×D3×#168 | semidirect |
| 129. C2 | C3⋊D3×#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C5×C3⋊D3 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| C2×C32×#168 | 2 |
| C3⋊D3×#168 | 2 |
| C2×D3×#168 | 3 |
| C2×C8×C3⋊D3 | 5 |