Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
546 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C3⋊D3 |
| commutator, socle, prime radical, cosocle | C23×C32 | C23 |
| Fitting | C2×C32×C4⋊C4 | C2 |
| hypercenter | C2×C4⋊C4 | C3⋊D3 |
| hypocenter | C32 | #395 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 28. C2×C32×C4 | Q8 | semidirect |
| 34. C2×C3⋊Dic3 | Q8 | semidirect |
| 67. C2×C3×C4 | Dic6 | semidirect |
| 100. C32 | #395 | semidirect |
| 114. C2×C4 | #634 | semidirect |
| 131. C3 | #4979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#634 | 2 |
| C2×C32×C4⋊C4 | 2 |
| C2×#3750 | 2 |
| #63658 | 2 |
| #4979 | 3 |