Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 9. C3×C9×Q16 | C4 | semidirect |
| 46. C9×Q16 | Dic3 | semidirect |
| 59. C3⋊Dic9 | Q16 | direct (N × H) |
| 94. C3×Q16 | Dic9 | semidirect |
| 127. C3×C9 | C4×Q16 | semidirect |
| 153. Q16 | C3⋊Dic9 | direct (N × H) |
| 175. C9 | Dic3×Q16 | semidirect |
| 198. C3 | Q16×Dic9 | 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 |
| Q8×C3⋊Dic9 | 2 |
| #11720582 | 2 |
| #11720541 | 2 |
| C8×C3⋊Dic9 | 2 |
| Q16×C3⋊Dic3 | 3 |
| Q16×Dic9 | 3 |