Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
702 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 124 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. C22×AΓL(1,𝔽9) | C2 | semidirect |
| 2. C2×C4×PSU(3,𝔽2) | C2 | semidirect |
| 4. C2×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. C2×GO+(4,𝔽2)⋊C4 | C2 | semidirect |
| 6. #10596410 | C2 | direct (N × H) |
| 12. C2×AΓL(1,𝔽9) | C22 | semidirect |
| 19. C4×PSU(3,𝔽2) | C22 | semidirect |
| 22. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 23. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 31. C2×PSU(3,𝔽2) | D4 | semidirect |
| 73. PSU(3,𝔽2) | C2×D4 | semidirect |
| 79. C2×C32×C4 | SD16 | semidirect |
| 80. C2×C3⋊Dic3 | SD16 | semidirect |
| 81. C4×C3⋊D3 | SD16 | semidirect |
| 114. C32×C4 | C2×SD16 | semidirect |
| 115. C3⋊Dic3 | C2×SD16 | semidirect |
| 147. C2×C32 | #460 | semidirect |
| 149. C3⋊D3 | #460 | semidirect |
| 196. C32 | C2×#460 | semidirect |
| 225. C2×C4 | AΓL(1,𝔽9) | semidirect |
| 251. C4 | C2×AΓL(1,𝔽9) | semidirect |
| 257. C2 | #10596410 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×AΓL(1,𝔽9) | 2 |
| C2×C4×PSU(3,𝔽2) | 2 |
| C2×#64231 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10596410 | 2 |
| C2×#460 | 9 |