Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 1. C2×C3×Q8×C9 | C2 | semidirect |
| 3. #88536 | C2 | semidirect |
| 4. C4×C3⋊Dic9 | C2 | semidirect |
| 17. C2×Q8×C9 | D3 | semidirect |
| 44. C2×C3×Q8 | D9 | semidirect |
| 65. C3×C9 | #124 | semidirect |
| 84. C2×Q8 | C3⋊D9 | semidirect |
| 101. C9 | #947 | semidirect |
| 120. C3 | #63509 | 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 |
| #64156 | 3 |
| #63509 | 3 |