Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
920 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 192 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 |
|---|---|---|
| 68. C33×C4 | Q16 | semidirect |
| 150. C32×C4 | Dic12 | semidirect |
| 151. C32×C4 | #216 | semidirect |
| 168. C33 | #462 | semidirect |
| 227. C3×C4 | #3719 | semidirect |
| 228. C3×C4 | #3746 | semidirect |
| 239. C32 | #4849 | semidirect |
| 240. C32 | #5031 | semidirect |
| 266. C4 | #88800 | semidirect |
| 270. C3 | #10590385 | semidirect |
| 271. C3 | #10592548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×C4×#634 | 2 |
| C2×#88800 | 2 |
| C32×C4⋊(C3⋊C8) | 2 |
| #11722042 | 2 |
| #10592548 | 3 |
| #10590385 | 3 |