Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
402 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 83 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×#63646 | C2 | semidirect |
| 3. C3×#63639 | C2 | semidirect |
| 17. #63646 | D3 | semidirect |
| 18. #63639 | D3 | semidirect |
| 179. C33 | #361 | semidirect |
| 274. C32 | #4495 | semidirect |
| 275. C32 | #4516 | semidirect |
| 276. C32 | #4563 | semidirect |
| 311. C3 | #10589126 | semidirect |
| 312. C3 | #10589127 | semidirect |
| 313. C3 | #10589128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3745 | 2 |
| C3×#63646 | 2 |
| C3×#63639 | 2 |
| #10589128 | 3 |
| #10589127 | 3 |
| #10589126 | 3 |