Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
232 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 111 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. #67464 | C2 | semidirect |
| 66. C3⋊C16 | M16 | semidirect |
| 162. C3 | #12020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1566 | 2 |
| C4×#812 | 2 |
| #69730 | 2 |
| #67464 | 2 |
| #12020 | 3 |