Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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. #4975 | C2 | semidirect |
| 5. C3×#340 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 27. #340 | D3 | semidirect |
| 228. C3 | #2071 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#821 | 2 |
| #4988 | 2 |
| #4975 | 2 |
| C2×#809 | 2 |
| C3×#340 | 2 |
| #4550 | 2 |
| #4529 | 2 |
| #2071 | 3 |