Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
528 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 132 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×C3⋊D3 |
| commutator, socle, prime radical, cosocle | C22×C33 | C23 |
| Fitting | C2×C33×C4 | C22 |
| hypercenter | C2×C4 | D3×C3⋊D3 |
| hypocenter | C33 | C4⋊Q8 |
| LCS | G ▷ C22×C33 ▷ C33 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 24. C3⋊(C3⋊Dic3) | Q8 | semidirect |
| 68. C33 | C4⋊Q8 | semidirect |
| 107. C32 | #944 | semidirect |
| 108. C32 | #944 | semidirect |
| 127. C3 | #63873 | semidirect |
| 128. C3 | #64153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#634 | 2 |
| C2×C32×Dic6 | 2 |
| C4×C3⋊(C3⋊Dic3) | 2 |
| #88806 | 2 |
| #64153 | 3 |
| #63873 | 3 |