Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
286 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | C3⋊S4 |
| commutator, hypocenter | C3×A4 | C2×C16 |
| Frattini | C8 | C2×C3⋊S4 |
| Fitting | C23×C3×C8 | D3 |
| socle | C24×C3 | C3⋊C8 |
| prime radical | C22×C3×A4 | C8 |
| cosocle | C3×C8×A4 | C22 |
| LCS | G ▷ C3×A4 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊(A4⋊C16) | C2 | direct (N × H) |
| 39. C2×C3×A4 | C16 | semidirect |
| 73. C3×A4 | C2×C16 | semidirect |
| 92. C23×C3 | C3⋊C16 | semidirect |
| 94. C2×A4 | C3⋊C16 | semidirect |
| 140. C22×C3 | C2×C3⋊C16 | semidirect |
| 142. A4 | C2×C3⋊C16 | semidirect |
| 153. C23 | C3⋊(C3⋊C16) | semidirect |
| 173. C2×C3 | A4⋊C16 | semidirect |
| 182. C22 | C2×C3⋊(C3⋊C16) | semidirect |
| 189. C3 | C2×A4⋊C16 | semidirect |
| 193. C2 | C3⋊(A4⋊C16) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×A4 | 2 |
| C3⋊(A4⋊C16) | 2 |
| C2×A4⋊C16 | 3 |
| C2×#4549 | 3 |
| C2×C3⋊(C3⋊C16) | 4 |