Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
608 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 128 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×#6308 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. #88803 | C2 | semidirect |
| 20. C3×C4×Dic3 | D3 | semidirect |
| 56. C4×Dic3 | C3⋊D3 | semidirect |
| 73. C33 | #124 | semidirect |
| 117. C32 | #875 | semidirect |
| 118. C32 | #936 | semidirect |
| 140. C3 | #63860 | semidirect |
| 141. C3 | #64084 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6308 | 2 |
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C32×C4×Dic3 | 2 |
| #88803 | 2 |
| #64084 | 3 |
| #63860 | 3 |