Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
241 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D32 |
| commutator, socle | C2×C32 | C22×C16 |
| Fitting | C32×C32 | C22 |
| prime radical | C2×D32 | C16 |
| cosocle | C32×C16 | C23 |
| hypercenter | C32 | D32 |
| hypocenter | C32 | C2×M64 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C16 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊D3×C32 | C2 | semidirect |
| 3. C3×#4447 | C2 | semidirect |
| 4. #10589068 | C2 | semidirect |
| 5. #10589067 | C2 | semidirect |
| 12. C32×C32 | C22 | semidirect |
| 13. C3⋊(C3⋊C32) | C22 | semidirect |
| 14. C3×C3⋊C32 | C22 | semidirect |
| 19. #4447 | D3 | semidirect |
| 42. C3×C32 | C2×D3 | semidirect |
| 45. C3⋊C32 | C2×D3 | semidirect |
| 86. C32 | D32 | semidirect |
| 102. C3⋊D3 | M64 | semidirect |
| 123. C32 | C2×M64 | semidirect |
| 145. C3 | D3×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D32×C16 | 2 |
| C3⋊D3×C32 | 2 |
| C3×#4447 | 2 |
| #10589068 | 2 |
| #10589067 | 2 |
| D3×M64 | 3 |