Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
882 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 231 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 | C23×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Fitting | C2×C32×#41 | C2 |
| hypercenter | C2×#41 | C3⋊D3 |
| hypocenter | C32 | #537 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×#41 | C2 | semidirect |
| 2. C2×#3828 | C2 | semidirect |
| 3. #64155 | C2 | semidirect |
| 4. #64148 | C2 | semidirect |
| 5. #64147 | C2 | semidirect |
| 6. #64139 | C2 | semidirect |
| 7. C2×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 8. #64133 | C2 | semidirect |
| 28. C2×C3×#41 | D3 | semidirect |
| 43. C2×C32×C4 | D4 | semidirect |
| 90. C2×#41 | C3⋊D3 | semidirect |
| 104. C2×C3×C4 | #67 | semidirect |
| 155. C32 | #537 | semidirect |
| 171. C2×C4 | #638 | semidirect |
| 196. C3 | #5833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41 | 2 |
| C2×#3828 | 2 |
| #64155 | 2 |
| #64148 | 2 |
| #64147 | 2 |
| #64139 | 2 |
| C2×C4⋊(C3⋊Dic3) | 2 |
| #64133 | 2 |
| #5833 | 3 |