Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
370 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 13. #64222 | C4 | semidirect |
| 31. #3777 | Q8 | semidirect |
| 137. C32 | #1988 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64222 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C4×#3777 | 2 |
| #10593166 | 2 |
| #1988 | 9 |