Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
588 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 128 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. #11722199 | C2 | semidirect |
| 4. C3×#63656 | C2 | semidirect |
| 5. #11722014 | C2 | semidirect |
| 6. #11722013 | C2 | semidirect |
| 30. #63656 | D3 | direct (N × H) |
| 123. C32×D3 | Q32 | semidirect |
| 173. C33 | C2×Q32 | semidirect |
| 203. C3×D3 | #829 | semidirect |
| 233. C32 | D3×Q32 | semidirect |
| 234. C32 | C2×#829 | semidirect |
| 250. D3 | #63656 | direct (N × H) |
| 259. C3 | D3×#829 | semidirect |
| 260. C3 | C2×#63656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D3×Q16 | 2 |
| D3×#3746 | 2 |
| #11722199 | 2 |
| C3×#63656 | 2 |
| #11722014 | 2 |
| #11722013 | 2 |
| D3×C3⋊(C3⋊C16) | 2 |
| C2×#63656 | 3 |
| D3×#829 | 3 |