Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
343 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 75 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×#3746⋊C3 | C2 | semidirect |
| 3. C2×#88386 | C2 | semidirect |
| 4. #11720249 | C2 | direct (N × H) |
| 13. #3746⋊C3 | C22 | semidirect |
| 14. #88386 | C22 | semidirect |
| 15. C2×#3746 | D3 | semidirect |
| 44. #3746 | C2×D3 | semidirect |
| 95. C2×H(3,𝔽3) | SD32 | semidirect |
| 143. H(3,𝔽3) | C2×SD32 | semidirect |
| 176. C2×C32 | #827 | semidirect |
| 177. C2×C32 | #828 | semidirect |
| 212. C32 | C2×#827 | semidirect |
| 213. C32 | C2×#828 | semidirect |
| 245. C2 | #11720249 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3745⋊C3 | 2 |
| C2×#3746⋊C3 | 2 |
| C2×#88386 | 2 |
| #11720249 | 2 |
| C2×#63549 | 3 |
| C2×#63548 | 3 |