Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 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 |
|---|---|---|
| 1. C2×C3×#131 | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C22×D24 | C2 | semidirect |
| 4. #5142 | C2 | direct (N × H) |
| 5. C2×#823 | C2 | semidirect |
| 6. C2×#819 | C2 | semidirect |
| 11. C3×#131 | C22 | semidirect |
| 17. #949 | C22 | semidirect |
| 24. C2×D24 | C22 | semidirect |
| 25. #823 | C22 | semidirect |
| 26. #819 | C22 | semidirect |
| 29. C2×#131 | D3 | semidirect |
| 76. #131 | C2×D3 | semidirect |
| 192. C2×C3 | #472 | semidirect |
| 210. C3 | C2×#472 | semidirect |
| 215. C2 | #5142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#949 | 2 |
| C22×D24 | 2 |
| #5142 | 2 |
| C2×#823 | 2 |
| C2×#819 | 2 |
| C2×#472 | 3 |