Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
160 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 33 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 |
|---|---|---|
| 5. C32×C5×Q8 | C4 | semidirect |
| 9. C5×#634 | C4 | semidirect |
| 35. C32×Q8 | Dic5 | semidirect |
| 39. #634 | Dic5 | semidirect |
| 47. C32×C5 | #103 | semidirect |
| 50. C5×Q8 | #157 | semidirect |
| 91. C32 | #3967 | semidirect |
| 94. Q8 | #4379 | semidirect |
| 102. C5 | #63784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×Q8×C3⋊D3 | 2 |
| C4⋊#4379 | 2 |
| #10624106 | 2 |
| #63784 | 5 |
| #3967 | 9 |