Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
237 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4×C8 | D32 |
| commutator, hypocenter | C32 | C8×C16 |
| Fitting, cosocle | C32×C4×C8 | C22 |
| socle, prime radical | C22×C32 | C4×C8 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. C3⋊(C3⋊C16) | C8 | semidirect |
| 22. C3×C3⋊C16 | C8 | semidirect |
| 38. C3×C3⋊C8 | C16 | semidirect |
| 57. C3⋊C16 | C3⋊C8 | direct (N × H) |
| 79. C3⋊C8 | C3⋊C16 | direct (N × H) |
| 100. C32 | C8×C16 | semidirect |
| 117. C3 | C8×C3⋊C16 | semidirect |
| 118. C3 | C16×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊(C3⋊C16) | 2 |
| C3×C4×C3⋊C16 | 2 |
| C3×C8×C3⋊C8 | 2 |
| C16×C3⋊C8 | 3 |
| C8×C3⋊C16 | 3 |