Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
136 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | Dic32 |
| commutator | C32×C4 | C4×C8 |
| Frattini, hypercenter | C2×C16 | D32 |
| Fitting, cosocle | C2×C32×C16 | C22 |
| socle | C2×C32 | #346 |
| prime radical | C22×C32 | M32 |
| hypocenter | C32 | #1398 |
| LCS | G ▷ C32×C4 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ C2×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C3⋊(C3⋊C32) | C4 | semidirect |
| 10. C3×C3⋊C32 | C4 | semidirect |
| 36. C3⋊C32 | Dic3 | semidirect |
| 101. C32 | #1398 | semidirect |
| 118. C3 | #67519 | semidirect |
| 119. C3 | #67600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589365 | 2 |
| C3×#4502 | 2 |
| C3×#4499 | 2 |
| #67600 | 3 |
| #67519 | 3 |