Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 266 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. C3×C4×M16 | C2 | semidirect |
| 3. #4924 | C2 | semidirect |
| 4. #4459 | C2 | semidirect |
| 5. #4456 | C2 | semidirect |
| 26. C4×M16 | D3 | semidirect |
| 93. D12 | M16 | semidirect |
| 99. Dic6 | M16 | semidirect |
| 199. C3 | #1489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#235 | 2 |
| C3×C4×M16 | 2 |
| #4924 | 2 |
| #4459 | 2 |
| #4456 | 2 |
| #1489 | 3 |