Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1010 conjugacy classes of subgroups; only the 273 normal subgroups are shown.
This group has 1010 conjugacy classes of subgroups — too many to draw. Only its 273 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. C22×C3×Q8×C9 | C2 | semidirect |
| 3. #11720572 | C2 | semidirect |
| 13. C22×Q8×C9 | D3 | semidirect |
| 20. C22×C3⋊D9 | Q8 | semidirect |
| 46. C22×C3×Q8 | D9 | semidirect |
| 101. C22×Q8 | C3⋊D9 | semidirect |
| 104. C3×C9 | #393 | semidirect |
| 153. C9 | #5231 | semidirect |
| 179. C3 | #10588911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8×C9 | 2 |
| C2×#88536 | 2 |
| #11720572 | 2 |
| #10592930 | 3 |
| #10588911 | 3 |