Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
444 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 1. C2×#67141 | C2 | semidirect |
| 3. #10623906 | C2 | semidirect |
| 4. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 6. #10623774 | C2 | semidirect |
| 29. C2×C32×D5 | Q8 | semidirect |
| 41. C4⋊(C3⋊Dic3) | D5 | semidirect |
| 77. C2×C3×D5 | Dic6 | semidirect |
| 91. C32×C5 | C22⋊Q8 | semidirect |
| 128. C2×D5 | #634 | semidirect |
| 146. C3×C5 | #878 | semidirect |
| 161. C32 | #4042 | semidirect |
| 175. C5 | #64087 | semidirect |
| 186. C3 | #91430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67141 | 2 |
| C2×D5×C3⋊Dic3 | 2 |
| #10623906 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C32×#685 | 2 |
| #10623774 | 2 |
| #10623770 | 2 |
| #91430 | 3 |
| #64087 | 5 |