Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
318 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 116 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. #10588220 | C2 | semidirect |
| 180. C9 | #1531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#533 | 2 |
| #10588606 | 2 |
| C2×#63362 | 2 |
| #10588220 | 2 |
| #71822 | 3 |