Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
357 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 357 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 186. C9 | #2072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63376 | 2 |
| #10588615 | 2 |
| #10588609 | 2 |
| C9×#336 | 2 |
| #10588229 | 2 |
| #68636 | 3 |