Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
298 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 123 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. C3 | #12881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4511 | 2 |
| #69804 | 2 |
| C3×#1375 | 2 |
| #67812 | 2 |
| #67663 | 2 |
| #12881 | 3 |