Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
294 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 122 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×C3⋊(C3⋊#168) | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. #10623796 | C2 | direct (N × H) |
| 12. C3⋊(C3⋊#168) | C22 | semidirect |
| 13. C3×C3⋊#168 | C22 | semidirect |
| 21. C2×C3⋊#168 | D3 | semidirect |
| 49. C3⋊#168 | C2×D3 | semidirect |
| 53. C2×C32×C5 | M16 | semidirect |
| 91. C32×C5 | C2×M16 | semidirect |
| 109. C2×C3×C5 | ΓL(1,𝔽25) | semidirect |
| 110. C2×C3×C5 | #208 | semidirect |
| 136. C2×C32 | #681 | semidirect |
| 144. C3×C5 | C2×ΓL(1,𝔽25) | semidirect |
| 145. C3×C5 | C2×#208 | semidirect |
| 162. C2×C5 | #3711 | semidirect |
| 164. C32 | C2×#681 | semidirect |
| 175. C2×C3 | #6650 | semidirect |
| 176. C2×C3 | #6710 | semidirect |
| 180. C5 | C2×#3711 | semidirect |
| 188. C3 | C2×#6650 | semidirect |
| 189. C3 | C2×#6710 | semidirect |
| 191. C2 | #10623796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×C5×D3 | 2 |
| C2×C3⋊(C3⋊#168) | 2 |
| C2×C3×C3⋊#168 | 2 |
| #10623796 | 2 |
| C2×#6710 | 3 |
| C2×#6650 | 3 |
| C2×#3711 | 5 |