Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×C3×Q8×C9 | C2 | semidirect |
| 4. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 5. #88534 | C2 | semidirect |
| 20. C2×Q8×C9 | D3 | semidirect |
| 28. C2×C3⋊D9 | Q8 | semidirect |
| 53. C2×C3×Q8 | D9 | semidirect |
| 80. C3×C9 | C22⋊Q8 | semidirect |
| 103. C2×Q8 | C3⋊D9 | semidirect |
| 125. C9 | #946 | semidirect |
| 149. C3 | #63508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C2×C4×C3⋊D9 | 2 |
| #88536 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| #88534 | 2 |
| #64155 | 3 |
| #63508 | 3 |