Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1976 conjugacy classes of subgroups; only the 281 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 281 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C3⋊S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Frattini | C2 | C23×C3⋊S4 |
| Fitting | C23×C3×Q8 | D3 |
| socle | C24×C3 | S4 |
| prime radical | C23×C3×SL(2,𝔽3) | C2 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C24 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C3⋊#226 | C2 | direct (N × H) |
| 7. C2×C3⋊#226 | C22 | direct (N × H) |
| 18. C3⋊#226 | C23 | direct (N × H) |
| 71. C23×C3 | #226 | semidirect |
| 100. C22×C3 | C2×#226 | semidirect |
| 107. C23 | C3⋊#226 | direct (N × H) |
| 120. C2×C3 | C22×#226 | semidirect |
| 122. C22 | C2×C3⋊#226 | direct (N × H) |
| 128. C3 | C23×#226 | semidirect |
| 129. C2 | C22×C3⋊#226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×SL(2,𝔽3) | 2 |
| C22×C3⋊#226 | 2 |
| C23×#226 | 3 |
| C23×#216 | 3 |
| C23×C3⋊Dic3 | 4 |