Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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×C4×C3⋊D9 | C2 | semidirect |
| 3. C3×C9×C4⋊C4 | C2 | semidirect |
| 4. #88536 | C2 | semidirect |
| 5. #88536 | C2 | semidirect |
| 6. #88536 | C2 | semidirect |
| 7. #88534 | C2 | semidirect |
| 28. C9×C4⋊C4 | D3 | semidirect |
| 74. C3×C4⋊C4 | D9 | semidirect |
| 109. C3×C9 | #123 | semidirect |
| 141. C4⋊C4 | C3⋊D9 | semidirect |
| 170. C9 | #894 | semidirect |
| 202. C3 | #63456 | 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×C4×C3⋊D9 | 2 |
| C3×C9×C4⋊C4 | 2 |
| #88536 | 2 |
| #88534 | 2 |
| #64103 | 3 |
| #63456 | 3 |