Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
17388 conjugacy classes of subgroups; only the 4701 normal subgroups are shown.
This group has 17388 conjugacy classes of subgroups — too many to draw. Only its 4701 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×C3⋊D3 |
| commutator, socle, cosocle | C2×C32 | C26 |
| Fitting | C32×#585 | C2 |
| hypercenter | #585 | C3⋊D3 |
| hypocenter | C32 | 2−1+6 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×#585 | C2 | semidirect |
| 2. C3⋊D3×2−1+4 | C2 | semidirect |
| 3. #10596758 | C2 | semidirect |
| 4. #10596756 | C2 | semidirect |
| 5. C2×#64367 | C2 | semidirect |
| 7. C32×2−1+4 | C22 | semidirect |
| 8. C32×H(5,𝔽2) | C22 | semidirect |
| 9. C2×C32×#41 | C22 | semidirect |
| 10. #64367 | C22 | semidirect |
| 11. #64367 | C22 | semidirect |
| 12. #64366 | C22 | semidirect |
| 13. #41×C3⋊D3 | C22 | semidirect |
| 14. #64364 | C22 | semidirect |
| 15. C2×Q8×C3⋊D3 | C22 | semidirect |
| 16. #64361 | C22 | semidirect |
| 17. C2×#3830 | C22 | semidirect |
| 18. C2×#3828 | C22 | semidirect |
| 19. C22×#634 | C22 | semidirect |
| 20. C3×#585 | D3 | semidirect |
| 43. C3×2−1+4 | C2×D3 | semidirect |
| 44. C3×H(5,𝔽2) | C2×D3 | semidirect |
| 45. C2×C3×#41 | C2×D3 | semidirect |
| 71. #585 | C3⋊D3 | semidirect |
| 101. 2−1+4 | C2×C3⋊D3 | semidirect |
| 104. H(5,𝔽2) | C2×C3⋊D3 | semidirect |
| 108. C2×#41 | C2×C3⋊D3 | semidirect |
| 151. C32 | 2−1+6 | semidirect |
| 175. C3 | #87572 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#585 | 2 |
| C3⋊D3×2−1+4 | 2 |
| #10596758 | 2 |
| #10596756 | 2 |
| C2×#64367 | 2 |
| #87572 | 3 |