Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
876 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C32×C4 | C23 |
| commutator | C23 | C22×C32×C4 |
| Frattini, cosocle | C22×C4 | C23×C32 |
| socle | C23×C32 | C22×C4 |
| prime radical | C24×C32 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C32×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×#336 | C2 | semidirect |
| 4. C3×#1818 | C3 | direct (N × H) |
| 14. C3×#336 | C2×C3 | semidirect |
| 26. #1818 | C32 | direct (N × H) |
| 48. #336 | C2×C32 | semidirect |
| 112. C32 | #1818 | direct (N × H) |
| 138. C3 | C3×#1818 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#117 | 2 |
| C2×C32×C22⋊C8 | 2 |
| C32×#336 | 2 |
| C3×#1818 | 3 |