Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10624098 | C2 | semidirect |
| 4. C23×C32×C5 | C4 | semidirect |
| 8. C2×C32×Dic5 | C4 | semidirect |
| 22. C23×C3×C5 | Dic3 | semidirect |
| 26. C2×C3×Dic5 | Dic3 | semidirect |
| 35. C23×C32 | AGL(1,𝔽5) | semidirect |
| 48. C32×C5 | #99 | semidirect |
| 49. C23×C5 | C3⋊Dic3 | semidirect |
| 53. C2×Dic5 | C3⋊Dic3 | semidirect |
| 67. C23×C3 | ΓL(1,𝔽16) | semidirect |
| 84. C3×C5 | #834 | semidirect |
| 96. C32 | #4011 | semidirect |
| 98. C23 | C3⋊ΓL(1,𝔽16) | semidirect |
| 106. C5 | #63661 | semidirect |
| 114. C3 | #91240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊D5 | 2 |
| #10624098 | 2 |
| #91240 | 3 |
| #63661 | 5 |