Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#924 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. C3×#407 | C2 | semidirect |
| 5. #5133 | C2 | semidirect |
| 6. #4739 | C2 | semidirect |
| 7. #4733 | C2 | semidirect |
| 8. #4731 | C2 | semidirect |
| 20. C22×Dic6 | C22 | semidirect |
| 21. C2×C3×M16 | C22 | semidirect |
| 23. C2×C4⋊Dic3 | C22 | semidirect |
| 27. #924 | C22 | semidirect |
| 30. C2×Dic12 | C22 | semidirect |
| 31. C2×#204 | C22 | semidirect |
| 33. C3×C22⋊C8 | C22 | semidirect |
| 34. #821 | C22 | semidirect |
| 35. #816 | C22 | semidirect |
| 43. #407 | D3 | semidirect |
| 101. C2×M16 | C2×D3 | semidirect |
| 112. C22⋊C8 | C2×D3 | semidirect |
| 204. C22×C3 | #137 | semidirect |
| 276. C22 | #909 | semidirect |
| 285. C3 | #3007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#235 | 2 |
| C2×#924 | 2 |
| C2×#909 | 2 |
| C3×#407 | 2 |
| #5133 | 2 |
| #4739 | 2 |
| #4733 | 2 |
| #4731 | 2 |
| #3007 | 3 |