Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
356 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 94 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. C33×M16 | C2 | semidirect |
| 3. C3×#3748 | C2 | semidirect |
| 4. #63650 | C3 | direct (N × H) |
| 15. C32×M16 | D3 | semidirect |
| 16. C32×M16 | C2×C3 | semidirect |
| 17. #3748 | C2×C3 | semidirect |
| 47. C3×M16 | C3×D3 | semidirect |
| 48. C3×M16 | C3⋊D3 | semidirect |
| 64. C33 | #100 | semidirect |
| 89. M16 | C3×C3⋊D3 | semidirect |
| 104. C32 | #823 | semidirect |
| 105. C32 | C3×#100 | semidirect |
| 126. C3 | C3×#823 | semidirect |
| 127. C3 | #63650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C33×M16 | 2 |
| C3×#3748 | 2 |
| #63650 | 3 |
| C3×#823 | 3 |