Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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×C9×M16 | C2 | semidirect |
| 3. #88532 | C2 | semidirect |
| 16. C9×M16 | D3 | semidirect |
| 42. C3×M16 | D9 | semidirect |
| 57. C3×C9 | #100 | semidirect |
| 78. M16 | C3⋊D9 | semidirect |
| 90. C9 | #823 | semidirect |
| 108. C3 | #63383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C3×C9×M16 | 2 |
| #88532 | 2 |
| #63650 | 3 |
| #63383 | 3 |