Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
426 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 174 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C32 | C22⋊C4 |
| commutator | C22 | C32×C42 |
| Frattini, cosocle | C24 | C22×C32 |
| prime radical | C24×C32 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C32 ◁ C24×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×#342 | C3 | direct (N × H) |
| 6. C22×C32×C4 | C4 | semidirect |
| 9. C32×C22⋊C4 | C4 | semidirect |
| 22. #342 | C32 | direct (N × H) |
| 25. C22×C3×C4 | C3×C4 | semidirect |
| 28. C3×C22⋊C4 | C3×C4 | semidirect |
| 61. C22×C4 | C32×C4 | semidirect |
| 64. C22⋊C4 | C32×C4 | semidirect |
| 77. C32 | #342 | direct (N × H) |
| 106. C3 | C3×#342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C22⋊C4 | 2 |
| C3×#342 | 3 |