Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
269 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 166. A4 | #1369 | semidirect |
| 205. C22 | #67514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11711530 | 2 |
| A4×#346 | 2 |
| #134662 | 3 |
| #67514 | 4 |