Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
426 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 99 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×#63645 | C2 | semidirect |
| 3. C2×C3×C3⋊(C3⋊C16) | C2 | semidirect |
| 11. C3×#3745 | C4 | semidirect |
| 17. #63645 | D3 | semidirect |
| 18. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 48. #3745 | Dic3 | semidirect |
| 190. C33 | #357 | semidirect |
| 300. C32 | #4491 | semidirect |
| 301. C32 | #4509 | semidirect |
| 302. C32 | #4562 | semidirect |
| 346. C3 | #10589114 | semidirect |
| 347. C3 | #10589115 | semidirect |
| 348. C3 | #10589116 | 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×#63645 | 2 |
| C2×C3×C3⋊(C3⋊C16) | 2 |
| #10589116 | 3 |
| #10589115 | 3 |
| #10589114 | 3 |