Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 91 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. D4×C3⋊Dic9 | C2 | semidirect |
| 3. C2×C3×#3672 | C2 | semidirect |
| 4. #11720967 | C2 | semidirect |
| 5. #11720295 | C2 | semidirect |
| 6. #11720276 | C2 | semidirect |
| 7. #11720273 | C2 | semidirect |
| 34. C2×#3672 | D3 | semidirect |
| 234. C3×C9 | #463 | semidirect |
| 339. C9 | #5165 | semidirect |
| 384. C3 | #10588833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×C3⋊Dic9 | 2 |
| C2×C9×#213 | 2 |
| C2×C3×#3672 | 2 |
| #11720967 | 2 |
| #11720295 | 2 |
| #11720276 | 2 |
| #11720273 | 2 |
| #10591476 | 3 |
| #10588833 | 3 |