Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
358 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C4×AGL(1,𝔽9) | C2 | semidirect |
| 4. #10593548 | C2 | semidirect |
| 6. #10593166 | C2 | semidirect |
| 7. #10593166 | C2 | semidirect |
| 19. GO+(4,𝔽2)⋊C4 | C4 | semidirect |
| 220. C32 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10593548 | 2 |
| #10593454 | 2 |
| #10593166 | 2 |
| #1934 | 9 |