Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1155 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1155 conjugacy classes of subgroups — too many to draw. Only its 221 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×#88552 | C2 | semidirect |
| 3. #11720580 | C2 | direct (N × H) |
| 5. C24×H(3,𝔽3) | C4 | semidirect |
| 9. C2×D4×H(3,𝔽3) | C4 | semidirect |
| 11. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 14. #88552 | C22 | semidirect |
| 24. C23×H(3,𝔽3) | C2×C4 | semidirect |
| 32. C2×C4×H(3,𝔽3) | C2×C4 | semidirect |
| 37. C24×C32 | Dic3 | semidirect |
| 41. C2×C32×D4 | Dic3 | semidirect |
| 43. C22×C32×C4 | Dic3 | semidirect |
| 75. C23×C32 | C2×Dic3 | semidirect |
| 83. C2×C32×C4 | C2×Dic3 | semidirect |
| 92. C2×H(3,𝔽3) | #99 | semidirect |
| 133. H(3,𝔽3) | C2×#99 | semidirect |
| 173. C2×C32 | #834 | semidirect |
| 175. C24 | #1084 | semidirect |
| 179. C2×D4 | #1084 | semidirect |
| 182. C22×C4 | #1084 | semidirect |
| 217. C32 | C2×#834 | semidirect |
| 224. C23 | C2×#1084 | semidirect |
| 234. C2×C4 | C2×#1084 | semidirect |
| 272. C2 | #11720580 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| #11720580 | 2 |
| C2×C3×#834 | 3 |