Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#936 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. C2×C3×#100 | C2 | semidirect |
| 5. C2×#825 | C2 | semidirect |
| 6. #4746 | C2 | direct (N × H) |
| 16. C22×Dic6 | C22 | semidirect |
| 17. C2×C3×M16 | C22 | semidirect |
| 20. #936 | C22 | semidirect |
| 21. C2×C4×Dic3 | C22 | semidirect |
| 23. #909 | C22 | semidirect |
| 26. C3×#100 | C22 | semidirect |
| 27. #825 | C22 | semidirect |
| 33. C2×#100 | D3 | semidirect |
| 62. C2×Dic6 | C23 | semidirect |
| 64. C3×M16 | C23 | semidirect |
| 68. C4×Dic3 | C23 | semidirect |
| 84. C2×M16 | C2×D3 | semidirect |
| 90. #100 | C2×D3 | semidirect |
| 156. M16 | C22×D3 | semidirect |
| 213. C2×C3 | #455 | semidirect |
| 232. C3 | C2×#455 | semidirect |
| 237. C2 | #4746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1004 | 2 |
| C2×#936 | 2 |
| C2×#909 | 2 |
| C2×C3×#100 | 2 |
| C2×#825 | 2 |
| #4746 | 2 |
| C2×#455 | 3 |