Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
378 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 11. C3×#3746 | C4 | semidirect |
| 48. #3746 | Dic3 | semidirect |
| 179. C33 | #358 | semidirect |
| 277. C32 | #4492 | semidirect |
| 278. C32 | #4503 | semidirect |
| 279. C32 | #4564 | semidirect |
| 317. C3 | #10589117 | semidirect |
| 318. C3 | #10589118 | semidirect |
| 319. C3 | #10589119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3746 | 2 |
| C3×#63645 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589119 | 3 |
| #10589118 | 3 |
| #10589117 | 3 |