Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #5119 | C2 | semidirect |
| 3. #5006 | C2 | semidirect |
| 4. #5002 | C2 | semidirect |
| 5. C3×H(3,ℤ/4) | C2 | semidirect |
| 23. H(3,ℤ/4) | D3 | semidirect |
| 144. C3 | #2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| #5119 | 2 |
| #5006 | 2 |
| #5002 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #2053 | 3 |