Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. C2×#816 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. #4977 | C2 | semidirect |
| 7. C2×#810 | C2 | semidirect |
| 15. #936 | C4 | semidirect |
| 216. C3 | #1958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#936 | 2 |
| C2×C3×#102 | 2 |
| C2×#832 | 2 |
| C2×#816 | 2 |
| C2×C8×Dic3 | 2 |
| #4977 | 2 |
| C2×#810 | 2 |
| #1958 | 3 |