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 |
|---|---|---|
| 2. C2×#6226 | C2 | semidirect |
| 3. C3×C42×C9 | C2 | semidirect |
| 4. #88536 | C2 | semidirect |
| 19. C42×C9 | D3 | semidirect |
| 48. C3×C42 | D9 | semidirect |
| 65. C3×C9 | #124 | semidirect |
| 87. C42 | C3⋊D9 | semidirect |
| 101. C9 | #875 | semidirect |
| 120. C3 | #63437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×#6226 | 2 |
| C3×C42×C9 | 2 |
| #88536 | 2 |
| #64084 | 3 |
| #63437 | 3 |