Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
182 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C2×C3 | C2×C3⋊S4 |
| commutator, cosocle, hypocenter | Q8⋊H(3,𝔽3) | C22 |
| Fitting | C32×#41 | D3 |
| prime radical | #41⋊H(3,𝔽3) | C2 |
| hypercenter | C3×C4 | C3⋊S4 |
| LCS | G ▷ Q8⋊H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #88610 | C2 | semidirect |
| 88. C32 | #984 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41⋊H(3,𝔽3) | 2 |
| #88610 | 2 |
| C3×#984 | 3 |
| C3×#951 | 3 |
| #6229 | 4 |