Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 87 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. C3×#63639 | C2 | semidirect |
| 3. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 18. #63639 | D3 | semidirect |
| 19. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 193. C33 | #350 | semidirect |
| 293. C32 | #4508 | semidirect |
| 294. C32 | #4515 | semidirect |
| 295. C32 | #4561 | semidirect |
| 331. C3 | #10589111 | semidirect |
| 332. C3 | #10589112 | semidirect |
| 333. C3 | #10589113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64110 | 2 |
| C3×#63639 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589113 | 3 |
| #10589112 | 3 |
| #10589111 | 3 |