Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#824 | C2 | semidirect |
| 100. C22×C3 | #101 | semidirect |
| 135. C22 | #824 | semidirect |
| 142. C3 | #1784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic6 | 2 |
| C3×#407 | 2 |
| #5207 | 2 |
| C2×#824 | 2 |
| #1784 | 3 |