Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C32×C4 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C23×C32 |
| socle | C2×C32 | #400 |
| prime radical | C23×C32 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C4 ◁ C22×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C3×#2102 | C3 | direct (N × H) |
| 34. #2102 | C32 | direct (N × H) |
| 129. C32 | #2102 | direct (N × H) |
| 154. C3 | C3×#2102 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#430 | 2 |
| C32×#423 | 2 |
| C32×#344 | 2 |
| C32×#339 | 2 |
| C32×H(3,ℤ/4) | 2 |
| C3×#2102 | 3 |