Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1176 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 210 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⋊#622 | C2 | semidirect |
| 3. C22×C3×#622 | C2 | semidirect |
| 4. C2×#88925 | C2 | direct (N × H) |
| 11. C2×C3⋊#622 | C22 | semidirect |
| 12. C2×C3×#622 | C22 | semidirect |
| 13. #88925 | C22 | direct (N × H) |
| 18. C22×#622 | D3 | semidirect |
| 27. C3⋊#622 | C23 | semidirect |
| 28. C3×#622 | C23 | semidirect |
| 43. C2×#622 | C2×D3 | semidirect |
| 44. C22×C33 | M16 | semidirect |
| 75. #622 | C22×D3 | semidirect |
| 77. C2×C33 | C2×M16 | semidirect |
| 100. C22×C32 | ΓL(1,𝔽25) | semidirect |
| 115. C33 | C22×M16 | semidirect |
| 141. C2×C32 | C2×ΓL(1,𝔽25) | semidirect |
| 158. C22×C3 | #3792 | semidirect |
| 171. C32 | C22×ΓL(1,𝔽25) | semidirect |
| 187. C2×C3 | C2×#3792 | semidirect |
| 192. C22 | #88925 | direct (N × H) |
| 199. C3 | C22×#3792 | semidirect |
| 201. C2 | C2×#88925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C3⋊Dic3 | 2 |
| C22×C3⋊#622 | 2 |
| C22×C3×#622 | 2 |
| C2×#88925 | 2 |
| C22×#3792 | 3 |
| C22×ΓL(1,𝔽25) | 9 |