Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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×#824 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4554 | C2 | semidirect |
| 7. #4552 | C2 | semidirect |
| 18. #951 | C4 | semidirect |
| 226. C3 | #1908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#951 | 2 |
| #5232 | 2 |
| C2×#824 | 2 |
| C2×#816 | 2 |
| #4554 | 2 |
| #4552 | 2 |
| #1908 | 3 |