Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
990 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 255 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 | C23×C32×C4 | C2 |
| hypercenter | C23×C4 | C3⋊D3 |
| hypocenter | C32 | #525 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C32×C4 | C2 | semidirect |
| 2. C2×#3828 | C2 | semidirect |
| 3. #64162 | C2 | semidirect |
| 4. #64139 | C2 | semidirect |
| 5. #64138 | C2 | semidirect |
| 6. C4×#638 | C2 | semidirect |
| 7. #64135 | C2 | semidirect |
| 8. #64133 | C2 | semidirect |
| 19. C2×C4⋊(C3⋊D3) | C22 | semidirect |
| 20. C2×C4×C3⋊D3 | C22 | semidirect |
| 21. C2×#634 | C22 | semidirect |
| 24. #3752 | C22 | semidirect |
| 25. C4⋊(C3⋊Dic3) | C22 | semidirect |
| 26. #3750 | C22 | semidirect |
| 27. C4×C3⋊Dic3 | C22 | semidirect |
| 28. C23×C3×C4 | D3 | semidirect |
| 44. C2×C32×C4 | D4 | semidirect |
| 79. C22×C32 | #41 | semidirect |
| 89. C23×C4 | C3⋊D3 | semidirect |
| 104. C2×C3×C4 | #67 | semidirect |
| 142. C22×C3 | #235 | semidirect |
| 152. C32 | #525 | semidirect |
| 168. C2×C4 | #638 | semidirect |
| 183. C22 | #3828 | semidirect |
| 191. C3 | #5791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C4 | 2 |
| C2×#3828 | 2 |
| #64162 | 2 |
| #64139 | 2 |
| #64138 | 2 |
| C4×#638 | 2 |
| #64135 | 2 |
| #64133 | 2 |
| #5791 | 3 |