Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
391 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 391 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 287. C32 | #1392 | semidirect |
| 337. C3 | #67693 | semidirect |
| 338. C3 | #67700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592936 | 2 |
| C3×#5237 | 2 |
| C3×#5234 | 2 |
| #67700 | 3 |
| #67693 | 3 |