Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C3×#417 | C2 | semidirect |
| 3. C2×#837 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. C2×#824 | C2 | semidirect |
| 6. #4973 | C2 | semidirect |
| 7. #4966 | C2 | semidirect |
| 13. #1010 | C4 | semidirect |
| 37. #417 | D3 | semidirect |
| 301. C3 | #1793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C3×#417 | 2 |
| C2×#837 | 2 |
| C2×#825 | 2 |
| C2×#824 | 2 |
| #4973 | 2 |
| #4966 | 2 |
| #1793 | 3 |