Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. C22×C3⋊Dic9 | C2 | semidirect |
| 3. C3×C9×C22⋊C4 | C2 | semidirect |
| 4. #88536 | C2 | semidirect |
| 5. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 22. C9×C22⋊C4 | D3 | semidirect |
| 57. C3×C22⋊C4 | D9 | semidirect |
| 80. C3×C9 | #123 | semidirect |
| 107. C22⋊C4 | C3⋊D9 | semidirect |
| 125. C9 | #886 | semidirect |
| 149. C3 | #63448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6233 | 2 |
| C22×C3⋊Dic9 | 2 |
| C3×C9×C22⋊C4 | 2 |
| #88536 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| #64095 | 3 |
| #63448 | 3 |