Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
378 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D32 |
| commutator, hypocenter | C32 | C2×C4×C8 |
| Frattini | C2×C4 | C2×D32 |
| Fitting | C22×C32×C4 | C22 |
| socle, prime radical | C23×C32 | C2×C4 |
| cosocle | C2×C32×C4 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #63553 | C2 | direct (N × H) |
| 9. C2×C3×C3⋊C8 | C4 | semidirect |
| 20. C2×C3⋊Dic3 | C8 | semidirect |
| 22. C3×C3⋊C8 | C2×C4 | semidirect |
| 34. C2×C3⋊C8 | Dic3 | semidirect |
| 41. C3⋊Dic3 | C2×C8 | semidirect |
| 59. C3⋊C8 | C2×Dic3 | semidirect |
| 60. C2×C32 | C4×C8 | semidirect |
| 82. C32 | C2×C4×C8 | semidirect |
| 93. C2×C3 | C8×Dic3 | semidirect |
| 103. C3 | C2×C8×Dic3 | semidirect |
| 104. C2 | #63553 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊Dic3 | 2 |
| C22×C3×C3⋊C8 | 2 |
| #63553 | 2 |
| C2×C8×Dic3 | 3 |