Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
662 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 115 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. C22×C3×ΓL(1,𝔽16) | C2 | semidirect |
| 3. #10623978 | C2 | direct (N × H) |
| 5. C22×C3⋊D15 | C4 | semidirect |
| 6. C22×C5×C3⋊D3 | C4 | semidirect |
| 9. C2×D5×C3⋊D3 | C4 | semidirect |
| 12. C2×C3×ΓL(1,𝔽16) | C22 | semidirect |
| 16. C22×ΓL(1,𝔽16) | D3 | semidirect |
| 21. C2×C3⋊D15 | C2×C4 | semidirect |
| 23. C2×C5×C3⋊D3 | C2×C4 | semidirect |
| 48. C2×ΓL(1,𝔽16) | C2×D3 | semidirect |
| 52. C2×C32×C5 | C22⋊C4 | semidirect |
| 56. C32×D5 | C22⋊C4 | semidirect |
| 66. C22×C3⋊D3 | AGL(1,𝔽5) | semidirect |
| 98. C32×C5 | C2×C22⋊C4 | semidirect |
| 116. C2×C3⋊D3 | C2×AGL(1,𝔽5) | semidirect |
| 121. C2×C3×C5 | (C2×D3)⋊C4 | semidirect |
| 127. C3×D5 | (C2×D3)⋊C4 | semidirect |
| 162. C2×C32 | C22⋊AGL(1,𝔽5) | semidirect |
| 170. C3×C5 | C2×(C2×D3)⋊C4 | semidirect |
| 196. C2×C5 | #3722 | semidirect |
| 199. D5 | #3722 | semidirect |
| 201. C32 | C2×C22⋊AGL(1,𝔽5) | semidirect |
| 217. C2×C3 | (C2×D3)⋊AGL(1,𝔽5) | semidirect |
| 223. C5 | C2×#3722 | semidirect |
| 236. C3 | C2×(C2×D3)⋊AGL(1,𝔽5) | semidirect |
| 241. C2 | #10623978 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D5×C3⋊D3 | 2 |
| C22×C3×ΓL(1,𝔽16) | 2 |
| #10623978 | 2 |
| C2×(C2×D3)⋊AGL(1,𝔽5) | 3 |
| C2×#3722 | 5 |