Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 25. C32×Q16 | C8 | semidirect |
| 26. #3756 | C8 | semidirect |
| 27. #3746 | C8 | semidirect |
| 86. Q16 | AGL(1,𝔽9) | semidirect |
| 101. C32 | #1579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×AGL(1,𝔽9) | 2 |
| Q16×#157 | 2 |
| Q8⋊AGL(1,𝔽9) | 2 |
| #10593252 | 2 |
| #10593251 | 2 |
| #1579 | 9 |