Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1092 conjugacy classes of subgroups; only the 343 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 343 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 |
|---|---|---|
| 23. C2×C3⋊(C3⋊Dic3) | C8 | semidirect |
| 82. C33 | #324 | semidirect |
| 115. C32 | #4469 | semidirect |
| 141. C3 | #10589335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88857 | 2 |
| C33×C22⋊C8 | 2 |
| #11722200 | 2 |
| #10589335 | 3 |