Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
334 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 77 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. C3×#407 | C2 | semidirect |
| 3. C2×C3⋊#95 | C2 | semidirect |
| 4. #4470 | C2 | semidirect |
| 5. #4467 | C2 | semidirect |
| 9. C2×#235 | C4 | semidirect |
| 12. #930 | C4 | semidirect |
| 17. #926 | C4 | semidirect |
| 18. #924 | C4 | semidirect |
| 25. #407 | D3 | semidirect |
| 45. C2×D12 | C2×C4 | semidirect |
| 47. C2×Dic6 | C2×C4 | semidirect |
| 55. C4⋊Dic3 | C2×C4 | semidirect |
| 56. C4⋊Dic3 | C2×C4 | semidirect |
| 230. C3 | #1504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5791 | 2 |
| C3×#407 | 2 |
| C2×C3⋊#95 | 2 |
| #4470 | 2 |
| #4467 | 2 |
| #1504 | 3 |