Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 3. C3×#6718 | C2 | direct (N × H) |
| 5. C2×#6718 | C3 | direct (N × H) |
| 21. #6718 | C2×C3 | direct (N × H) |
| 57. C2×C32×C5 | Q16 | semidirect |
| 94. C32×C5 | C2×Q16 | semidirect |
| 111. C2×C3×C5 | #216 | semidirect |
| 112. C2×C3×C5 | C3×Q16 | semidirect |
| 140. C2×C32 | #689 | semidirect |
| 147. C3×C5 | C2×#216 | semidirect |
| 148. C3×C5 | C2×C3×Q16 | semidirect |
| 163. C2×C5 | C3×#216 | semidirect |
| 165. C32 | C2×#689 | semidirect |
| 176. C2×C3 | C3×#689 | semidirect |
| 177. C2×C3 | #6718 | direct (N × H) |
| 180. C5 | C2×C3×#216 | semidirect |
| 187. C3 | C2×C3×#689 | semidirect |
| 188. C3 | C2×#6718 | direct (N × H) |
| 189. C2 | C3×#6718 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C5×Q8 | 2 |
| C2×C3×Dic30 | 2 |
| C3×#6718 | 2 |
| C2×C3×C3⋊#168 | 2 |
| C2×#6718 | 3 |
| C2×C3×#689 | 3 |
| C2×C3×#216 | 5 |