Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
604 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 106 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, cosocle | C22×C33 | C23 |
| Fitting | C2×C33×C4 | C22 |
| prime radical | C2×#6292 | C2 |
| hypercenter | C2×C4 | D3×C3⋊D3 |
| hypocenter | C33 | #123 |
| 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 |
|---|---|---|
| 2. C2×#6289 | C2 | semidirect |
| 3. #88859 | C2 | semidirect |
| 4. C3×#3752 | C2 | semidirect |
| 5. C32×C4⋊Dic3 | C2 | semidirect |
| 6. #88806 | C2 | semidirect |
| 7. #88803 | C2 | semidirect |
| 28. #3752 | D3 | semidirect |
| 31. C3×C4⋊Dic3 | D3 | semidirect |
| 86. C4⋊Dic3 | C3⋊D3 | semidirect |
| 120. C33 | #123 | semidirect |
| 194. C32 | #883 | semidirect |
| 195. C32 | #894 | semidirect |
| 232. C3 | #63854 | semidirect |
| 233. C3 | #64103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6292 | 2 |
| C2×#6289 | 2 |
| #88859 | 2 |
| C3×#3752 | 2 |
| C32×C4⋊Dic3 | 2 |
| #88806 | 2 |
| #88803 | 2 |
| #64103 | 3 |
| #63854 | 3 |