Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#825 | C2 | semidirect |
| 4. C4×C4⋊Dic3 | C2 | semidirect |
| 13. #875 | C4 | semidirect |
| 14. #874 | C4 | semidirect |
| 17. #869 | C4 | semidirect |
| 24. C4×M16 | D3 | semidirect |
| 39. C3×M16 | D4 | semidirect |
| 104. M16 | D12 | semidirect |
| 127. C3×C4 | #104 | semidirect |
| 175. C4 | #825 | semidirect |
| 178. C3 | #1980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C3×C4×M16 | 2 |
| C2×#825 | 2 |
| C4×C4⋊Dic3 | 2 |
| #1980 | 3 |