Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
930 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 235 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C24 |
| Frattini | C22 | C23×C3⋊D3 |
| Fitting | C2×C32×#41 | C2 |
| hypercenter | C2×#41 | C3⋊D3 |
| hypocenter | C32 | #532 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ 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. #64156 | C2 | semidirect |
| 4. #64153 | C2 | semidirect |
| 5. #64149 | C2 | semidirect |
| 6. #64148 | C2 | semidirect |
| 7. #64145 | C2 | semidirect |
| 8. C4×#638 | C2 | semidirect |
| 9. C2×C4×C3⋊Dic3 | C2 | semidirect |
| 30. C2×C3×#41 | D3 | semidirect |
| 46. C2×C32×C4 | D4 | semidirect |
| 91. C3⋊Dic3 | #41 | semidirect |
| 93. C2×#41 | C3⋊D3 | semidirect |
| 108. C2×C3×C4 | #67 | semidirect |
| 158. C32 | #532 | semidirect |
| 175. C2×C4 | #638 | semidirect |
| 197. C3 | #5832 | 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 |
| #64156 | 2 |
| #64153 | 2 |
| #64149 | 2 |
| #64148 | 2 |
| #64145 | 2 |
| C4×#638 | 2 |
| C2×C4×C3⋊Dic3 | 2 |
| #5832 | 3 |