Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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×C3×#137 | C2 | semidirect |
| 3. C2×#944 | C2 | semidirect |
| 4. C2×#942 | C2 | semidirect |
| 5. C2×#837 | C2 | semidirect |
| 6. #5205 | C2 | direct (N × H) |
| 7. C2×#825 | C2 | semidirect |
| 8. C2×#824 | C2 | semidirect |
| 24. C3×#137 | C22 | semidirect |
| 29. #944 | C22 | semidirect |
| 32. #942 | C22 | semidirect |
| 37. #837 | C22 | semidirect |
| 38. #825 | C22 | semidirect |
| 39. #824 | C22 | semidirect |
| 42. C2×#137 | D3 | semidirect |
| 123. #137 | C2×D3 | semidirect |
| 314. C2×C3 | #456 | semidirect |
| 334. C3 | C2×#456 | semidirect |
| 339. C2 | #5205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C2×C3×#137 | 2 |
| C2×#944 | 2 |
| C2×#942 | 2 |
| C2×#837 | 2 |
| #5205 | 2 |
| C2×#825 | 2 |
| C2×#824 | 2 |
| C2×#456 | 3 |