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 | C2×C32×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | C3⋊D3 |
| hypocenter | C32 | 2−1+6 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C32×2−1+4 | C2 | semidirect |
| 2. #10596760 | C2 | semidirect |
| 3. C3⋊D3×2−1+4 | C2 | semidirect |
| 4. #10596756 | C2 | semidirect |
| 5. C2×#64364 | C2 | semidirect |
| 7. C32×2−1+4 | C22 | semidirect |
| 8. C2×C32×#41 | C22 | semidirect |
| 9. C22×C32×Q8 | C22 | semidirect |
| 10. #64367 | C22 | semidirect |
| 11. #64366 | C22 | semidirect |
| 12. #41×C3⋊D3 | C22 | semidirect |
| 13. #64364 | C22 | semidirect |
| 14. #64364 | C22 | semidirect |
| 15. C2×#3832 | C22 | semidirect |
| 16. C2×Q8×C3⋊D3 | C22 | semidirect |
| 17. #64361 | C22 | semidirect |
| 18. C2×#3828 | C22 | semidirect |
| 19. C2×C3×2−1+4 | D3 | semidirect |
| 40. C3×2−1+4 | C2×D3 | semidirect |
| 41. C2×C3×#41 | C2×D3 | semidirect |
| 42. C22×C3×Q8 | C2×D3 | semidirect |
| 68. C2×2−1+4 | C3⋊D3 | semidirect |
| 94. 2−1+4 | C2×C3⋊D3 | semidirect |
| 100. C2×#41 | C2×C3⋊D3 | semidirect |
| 102. C22×Q8 | C2×C3⋊D3 | semidirect |
| 141. C32 | 2−1+6 | semidirect |
| 165. C3 | #87571 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×2−1+4 | 2 |
| #10596760 | 2 |
| C3⋊D3×2−1+4 | 2 |
| #10596756 | 2 |
| C2×#64364 | 2 |
| #87571 | 3 |