Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
606 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596542 | C2 | semidirect |
| 3. #10596484 | C2 | semidirect |
| 4. #10596417 | C2 | semidirect |
| 5. #10596410 | C2 | semidirect |
| 6. #10596408 | C2 | semidirect |
| 7. #10596402 | C2 | semidirect |
| 10. C2×AΓL(1,𝔽9) | C22 | semidirect |
| 16. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 17. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 19. C4×PSU(3,𝔽2) | C22 | semidirect |
| 26. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 27. C4×AGL(1,𝔽9) | C22 | semidirect |
| 28. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 84. C2×C32×C4 | SD16 | semidirect |
| 85. C2×C3⋊Dic3 | SD16 | semidirect |
| 86. C4×C3⋊D3 | SD16 | semidirect |
| 87. C4×C3⋊D3 | SD16 | semidirect |
| 224. C32 | #3208 | semidirect |
| 254. C2×C4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596542 | 2 |
| C2×#64231 | 2 |
| #10596484 | 2 |
| #10596417 | 2 |
| #10596410 | 2 |
| #10596408 | 2 |
| #10596402 | 2 |
| #3208 | 9 |