Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1089 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1089 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 1. H(3,𝔽3)×H(5,𝔽2) | C2 | semidirect |
| 2. #11721847 | C2 | semidirect |
| 3. #11720580 | C2 | semidirect |
| 5. C23×#272 | C22 | semidirect |
| 10. #88552 | C22 | semidirect |
| 12. C32×H(5,𝔽2) | D3 | semidirect |
| 16. C23×H(3,𝔽3) | D4 | semidirect |
| 24. C2×C4×H(3,𝔽3) | D4 | semidirect |
| 53. C23×C32 | #67 | semidirect |
| 61. C2×C32×C4 | #67 | semidirect |
| 93. H(5,𝔽2) | #272 | semidirect |
| 96. H(3,𝔽3) | B(4,𝔽2) | semidirect |
| 152. C32 | #5244 | semidirect |
| 156. C23 | #6235 | semidirect |
| 164. C2×C4 | #6235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×H(5,𝔽2) | 2 |
| #11721847 | 2 |
| #11720580 | 2 |
| C3×#5244 | 3 |