Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
570 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×C3×C9×Q16 | C2 | semidirect |
| 4. #11720582 | C2 | semidirect |
| 5. #11720541 | C2 | semidirect |
| 22. C2×C9×Q16 | D3 | semidirect |
| 61. C2×C3⋊D9 | Q16 | semidirect |
| 67. C2×C3×Q16 | D9 | semidirect |
| 140. C2×Q16 | C3⋊D9 | semidirect |
| 145. C3×C9 | #467 | semidirect |
| 204. C9 | #5188 | semidirect |
| 233. C3 | #10588868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11721856 | 2 |
| C2×C8×C3⋊D9 | 2 |
| #11720582 | 2 |
| #11720541 | 2 |
| #10592887 | 3 |
| #10588868 | 3 |