Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 122 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. #10588224 | C2 | semidirect |
| 166. C9 | #1556 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊Q8 | 2 |
| #10588606 | 2 |
| #10588224 | 2 |
| #71776 | 3 |