Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
200 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 59 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. C2×C3×Dic18 | C2 | semidirect |
| 3. #88532 | C2 | semidirect |
| 4. #88427 | C2 | semidirect |
| 5. #88423 | C2 | semidirect |
| 23. C2×Dic18 | D3 | semidirect |
| 86. C3×C9 | #137 | semidirect |
| 137. C9 | #942 | semidirect |
| 162. C3 | #63511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#235 | 2 |
| C2×C3×Dic18 | 2 |
| #88532 | 2 |
| #88427 | 2 |
| #88423 | 2 |
| #63827 | 3 |
| #63511 | 3 |