Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
300 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 1. C3×C9×C4⋊C4 | C2 | semidirect |
| 5. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 6. #88534 | C2 | semidirect |
| 7. C4×C3⋊Dic9 | C2 | semidirect |
| 24. C9×C4⋊C4 | D3 | semidirect |
| 61. C3×C4⋊C4 | D9 | semidirect |
| 96. C3×C9 | #126 | semidirect |
| 121. C4⋊C4 | C3⋊D9 | semidirect |
| 147. C9 | #898 | semidirect |
| 173. C3 | #63460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C4⋊C4 | 2 |
| #88536 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| #88534 | 2 |
| C4×C3⋊Dic9 | 2 |
| #64107 | 3 |
| #63460 | 3 |