Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
756 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 213 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×D3×M16 | C2 | semidirect |
| 3. C2×C3×#101 | C2 | semidirect |
| 4. C2×#836 | C2 | semidirect |
| 5. C2×#823 | C2 | semidirect |
| 6. #4751 | C2 | direct (N × H) |
| 21. D3×M16 | C22 | semidirect |
| 24. C3×#101 | C22 | semidirect |
| 25. #836 | C22 | semidirect |
| 26. #823 | C22 | semidirect |
| 31. C2×#101 | D3 | semidirect |
| 87. #101 | C2×D3 | semidirect |
| 211. C2×C3 | #413 | semidirect |
| 232. C3 | C2×#413 | semidirect |
| 237. C2 | #4751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#239 | 2 |
| C2×D3×M16 | 2 |
| C2×C3×#101 | 2 |
| C2×#836 | 2 |
| C2×#823 | 2 |
| #4751 | 2 |
| C2×#413 | 3 |