Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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. #4682 | C2 | semidirect |
| 5. #4681 | C2 | semidirect |
| 6. #4681 | C2 | semidirect |
| 7. C3×#322 | C2 | semidirect |
| 28. #322 | D3 | semidirect |
| 132. C3 | #1719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4694 | 2 |
| #4693 | 2 |
| #4682 | 2 |
| #4681 | 2 |
| C3×#322 | 2 |
| #1719 | 3 |