Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 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 |
|---|---|---|
| 2. C2×C3×M32 | C2 | semidirect |
| 3. #5106 | C2 | semidirect |
| 4. #4518 | C2 | semidirect |
| 9. C2×Dic12 | C4 | semidirect |
| 12. #904 | C4 | semidirect |
| 14. C2×D24 | C4 | semidirect |
| 17. C3×M32 | C22 | semidirect |
| 20. #817 | C22 | semidirect |
| 22. C2×M32 | D3 | semidirect |
| 61. M32 | C2×D3 | semidirect |
| 163. C3 | #2145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C2×C3×M32 | 2 |
| #5106 | 2 |
| #4518 | 2 |
| #2145 | 3 |