Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
486 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×C3×#3674 | C2 | semidirect |
| 4. C2×#88427 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720298 | C2 | semidirect |
| 34. C2×#3674 | D3 | semidirect |
| 97. C2×D3×C9 | Q16 | semidirect |
| 236. C3×C9 | #451 | semidirect |
| 315. C2×D3 | #3674 | semidirect |
| 336. C9 | #5186 | semidirect |
| 379. C3 | #10588907 | 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 |
| C2×C3×#3674 | 2 |
| #11720960 | 2 |
| C2×#88427 | 2 |
| #11720582 | 2 |
| #11720298 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #10591594 | 3 |
| #10588907 | 3 |