Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
600 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C3×C9×C22⋊Q8 | C2 | semidirect |
| 2. C2×#88548 | C2 | semidirect |
| 4. C2×#88532 | C2 | semidirect |
| 5. #11720582 | C2 | semidirect |
| 6. #11720528 | C2 | semidirect |
| 7. #11720525 | C2 | semidirect |
| 30. C9×C22⋊Q8 | D3 | semidirect |
| 52. C3⋊(C9⋊C8) | D4 | semidirect |
| 94. C3×C22⋊Q8 | D9 | semidirect |
| 200. C22⋊Q8 | C3⋊D9 | semidirect |
| 205. C3×C9 | #468 | semidirect |
| 288. C9 | #5049 | semidirect |
| 328. C3 | #10588732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊Q8 | 2 |
| C2×#88548 | 2 |
| #11721819 | 2 |
| C2×#88532 | 2 |
| #11720582 | 2 |
| #11720528 | 2 |
| #11720525 | 2 |
| #10592748 | 3 |
| #10588732 | 3 |