Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
143 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 143 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D9⋊A4 |
| commutator, cosocle, hypocenter | Q8×C9 | C22×C3 |
| Frattini, socle | C2×C3 | C2×D3×A4 |
| Fitting | C9×#41 | C2×C3 |
| hypercenter | C4 | D9⋊A4 |
| LCS | G ▷ Q8×C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #88683 | C2 | semidirect |
| 2. D9⋊SL(2,𝔽3) | C2 | semidirect |
| 4. #63716 | C3 | semidirect |
| 9. C9×#41 | C2×C3 | semidirect |
| 10. Q8×D9 | C2×C3 | semidirect |
| 69. #41 | AGL(1,ℤ/9) | semidirect |
| 81. C9 | 2−1+4⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88683 | 2 |
| D9⋊SL(2,𝔽3) | 2 |
| #1010⋊C3 | 3 |
| #63716 | 3 |
| C4⋊AGL(1,ℤ/9) | 4 |