Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
330 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 91 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×#67158 | C2 | semidirect |
| 5. #10623832 | C2 | semidirect |
| 6. #10623831 | C2 | semidirect |
| 7. #10623831 | C2 | semidirect |
| 37. C22×C32×C5 | Q8 | semidirect |
| 104. C22×C3×C5 | Dic6 | semidirect |
| 105. C22×C3×C5 | Dic6 | semidirect |
| 137. C32×C5 | C22⋊Q8 | semidirect |
| 149. C22×C32 | Dic10 | semidirect |
| 193. C22×C5 | #627 | semidirect |
| 213. C3×C5 | #878 | semidirect |
| 214. C3×C5 | #924 | semidirect |
| 223. C22×C3 | #1204 | semidirect |
| 224. C22×C3 | #1204 | semidirect |
| 245. C32 | #4024 | semidirect |
| 267. C5 | #63964 | semidirect |
| 270. C22 | #67158 | semidirect |
| 279. C3 | #91574 | semidirect |
| 280. C3 | #91576 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic15 | 2 |
| C2×#67158 | 2 |
| C5×#3757 | 2 |
| C3×#6719 | 2 |
| #10623832 | 2 |
| #10623831 | 2 |
| #91576 | 3 |
| #91574 | 3 |
| #63964 | 5 |