Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
476 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #11720581 | C2 | semidirect |
| 4. C3×#63394 | C2 | semidirect |
| 5. #11720299 | C2 | semidirect |
| 29. #63394 | D3 | direct (N × H) |
| 125. D3×C9 | #101 | semidirect |
| 174. C3×C9 | C2×#101 | semidirect |
| 249. C9 | D3×#101 | semidirect |
| 273. D3 | #63394 | direct (N × H) |
| 283. C3 | C2×#63394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8×C9 | 2 |
| D3×#3667 | 2 |
| #11720581 | 2 |
| C3×#63394 | 2 |
| #11720299 | 2 |
| D3×#836 | 3 |
| C2×#63394 | 3 |