Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C3×#543 | C2 | semidirect |
| 3. #4527 | C2 | semidirect |
| 10. #543 | D3 | semidirect |
| 14. C23×D3 | Q8 | semidirect |
| 20. C22×Dic3 | Q8 | semidirect |
| 99. C3 | #2032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#543 | 2 |
| C2×#806 | 2 |
| #4527 | 2 |
| #2032 | 3 |