Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
954 conjugacy classes of subgroups; only the 522 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 522 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 |
|---|---|---|
| 2. C3×Q8×Dic9 | C2 | semidirect |
| 5. #10589914 | C3 | direct (N × H) |
| 6. C2×C3×Q8×C9 | C4 | semidirect |
| 17. Q8×Dic9 | C2×C3 | semidirect |
| 34. C2×Q8×C9 | C3×C4 | semidirect |
| 73. C2×C3×Q8 | Dic9 | semidirect |
| 103. C3×C9 | #519 | semidirect |
| 127. C2×Q8 | C3×Dic9 | semidirect |
| 149. C9 | C3×#519 | semidirect |
| 170. C3 | #10589914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q8×C9 | 2 |
| C3×Q8×Dic9 | 2 |
| C3×#63488 | 2 |
| C3×#5812 | 3 |
| #10589914 | 3 |