Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2268 conjugacy classes of subgroups; only the 859 normal subgroups are shown.
This group has 2268 conjugacy classes of subgroups — too many to draw. Only its 859 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 |
|---|---|---|
| 4. #11722186 | C2 | direct (N × H) |
| 11. C2×#6308 | C4 | semidirect |
| 32. #6308 | C2×C4 | semidirect |
| 73. C2×C33 | #103 | semidirect |
| 101. C33 | C2×#103 | semidirect |
| 115. C2×C32 | #816 | semidirect |
| 139. C32 | C2×#816 | semidirect |
| 153. C2×C3 | #63643 | semidirect |
| 166. C3 | C2×#63643 | semidirect |
| 167. C2 | #11722186 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6308 | 2 |
| C22×C33×C8 | 2 |
| C2×C4⋊(C3⋊(C3⋊Dic3)) | 2 |
| #11722186 | 2 |
| C2×#63643 | 3 |