Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
354 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 354 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 |
|---|---|---|
| 173. C33 | #362 | semidirect |
| 260. C32 | #4496 | semidirect |
| 261. C32 | #4517 | semidirect |
| 262. C32 | #4565 | semidirect |
| 292. C3 | #10589129 | semidirect |
| 293. C3 | #10589130 | semidirect |
| 294. C3 | #10589131 | 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×#63646 | 2 |
| C3×#63639 | 2 |
| #10589131 | 3 |
| #10589130 | 3 |
| #10589129 | 3 |