Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
636 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 3. #10592730 | C2 | semidirect |
| 4. #10592719 | C2 | semidirect |
| 6. #10589401 | C2 | semidirect |
| 7. #10589401 | C2 | semidirect |
| 224. C32 | #1640 | semidirect |
| 267. C3 | #71945 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#559 | 2 |
| #10592769 | 2 |
| #10592730 | 2 |
| #10592719 | 2 |
| #10589410 | 2 |
| #10589401 | 2 |
| #71945 | 3 |