Finite Group DatabasebetaFinite Group DatabasebetaOrder 2160.
442 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 66 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⋊ΓL(1,𝔽16))⋊C3 | C2 | semidirect |
| 3. #11761932 | C2 | direct (N × H) |
| 5. C2×C5⋊#272 | C4 | semidirect |
| 6. C2×C5×#272 | C4 | semidirect |
| 8. D5×#272 | C4 | semidirect |
| 10. (C3⋊ΓL(1,𝔽16))⋊C3 | C22 | semidirect |
| 14. C2×C3⋊ΓL(1,𝔽16) | D3 | semidirect |
| 17. C2×C5×H(3,𝔽3) | C2×C4 | semidirect |
| 18. C5⋊#272 | C2×C4 | semidirect |
| 19. C5×#272 | C2×C4 | semidirect |
| 20. D5×H(3,𝔽3) | C2×C4 | semidirect |
| 37. C3⋊ΓL(1,𝔽16) | C2×D3 | semidirect |
| 40. C5×H(3,𝔽3) | C22×C4 | semidirect |
| 53. C2×#272 | AGL(1,𝔽5) | semidirect |
| 56. C2×C32×C5 | C4×D3 | semidirect |
| 63. C32×D5 | C4×D3 | semidirect |
| 91. C2×H(3,𝔽3) | C2×AGL(1,𝔽5) | semidirect |
| 93. #272 | C2×AGL(1,𝔽5) | semidirect |
| 97. C32×C5 | C2×C4×D3 | semidirect |
| 128. H(3,𝔽3) | C22×AGL(1,𝔽5) | semidirect |
| 148. C2×C32 | D3×AGL(1,𝔽5) | semidirect |
| 176. C2×C5 | #6199 | semidirect |
| 178. D5 | #6199 | semidirect |
| 181. C32 | C2×D3×AGL(1,𝔽5) | semidirect |
| 200. C5 | C2×#6199 | semidirect |
| 214. C2 | #11761932 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×#272 | 2 |
| C2×(C3⋊ΓL(1,𝔽16))⋊C3 | 2 |
| #11761932 | 2 |
| C2×D3×ΓL(1,𝔽16) | 3 |
| C2×#6199 | 5 |