Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1260 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 403 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×#88853 | C2 | semidirect |
| 3. #11722197 | C2 | direct (N × H) |
| 4. C2×C3⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 12. #88853 | C22 | semidirect |
| 13. C3⋊(C3⋊(C3⋊C16)) | C22 | semidirect |
| 57. C2×C33 | SD32 | semidirect |
| 77. C33 | C2×SD32 | semidirect |
| 88. C2×C32 | #827 | semidirect |
| 104. C32 | C2×#827 | semidirect |
| 115. C2×C3 | #63654 | semidirect |
| 123. C3 | C2×#63654 | semidirect |
| 125. C2 | #11722197 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D8 | 2 |
| C2×#88853 | 2 |
| #11722197 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| C2×#63654 | 3 |