Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 293 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 |
|---|---|---|
| 3. #5121 | C2 | semidirect |
| 4. #5106 | C2 | semidirect |
| 7. C2×C3×M16 | C4 | semidirect |
| 17. #818 | C22 | semidirect |
| 18. #817 | C22 | semidirect |
| 31. C3×M16 | C2×C4 | semidirect |
| 32. C2×C3×C8 | C2×C4 | semidirect |
| 41. C2×M16 | Dic3 | semidirect |
| 77. M16 | C2×Dic3 | semidirect |
| 78. C2×C8 | C2×Dic3 | semidirect |
| 128. C3 | #2911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| C2×#926 | 2 |
| #5121 | 2 |
| #5106 | 2 |
| #2911 | 3 |