Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 220 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. C2×#819 | C2 | semidirect |
| 4. #4517 | C2 | semidirect |
| 5. #4516 | C2 | semidirect |
| 23. C2×M32 | D3 | semidirect |
| 163. C3 | #2148 | 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 |
| C2×#819 | 2 |
| #4517 | 2 |
| #4516 | 2 |
| #2148 | 3 |