Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
157 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 157 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×(C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C22×C3 |
| Frattini | C2×C3 | C2×C3×S4 |
| Fitting | C32×#41 | D3 |
| socle | C2×C32 | C2×S4 |
| hypercenter | C3×C4 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#41⋊C9 | C2 | semidirect |
| 2. C3×#3689 | C2 | semidirect |
| 4. #63692 | C3 | direct (N × H) |
| 6. C3×Q8⋊C9 | C22 | semidirect |
| 13. #41⋊C9 | C2×C3 | semidirect |
| 14. #3689 | C2×C3 | semidirect |
| 28. Q8⋊C9 | C22×C3 | semidirect |
| 32. C3×#41 | D9 | semidirect |
| 75. #41 | C3×D9 | semidirect |
| 117. C3 | #63692 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#41⋊C9 | 2 |
| C3×#3689 | 2 |
| C3×#949 | 3 |
| #63692 | 3 |
| C3×D36 | 4 |