Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 3. #4551 | C2 | semidirect |
| 7. C22×C3×C8 | C4 | semidirect |
| 11. #926 | C4 | semidirect |
| 34. C22×C8 | Dic3 | semidirect |
| 114. C3 | #1735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C8 | 2 |
| C2×#926 | 2 |
| #4551 | 2 |
| #1735 | 3 |