Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
214 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #10593253 | C2 | semidirect |
| 5. #10593252 | C2 | semidirect |
| 32. C32×M16 | C8 | semidirect |
| 33. #3748 | C8 | semidirect |
| 34. #3743 | C8 | semidirect |
| 56. C32×C8 | C2×C8 | semidirect |
| 57. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 115. M16 | AGL(1,𝔽9) | semidirect |
| 135. C32 | #1565 | semidirect |
| 155. C8 | C2×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596484 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| M16×#157 | 2 |
| #10593253 | 2 |
| #10593252 | 2 |
| #1565 | 9 |