Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
280 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 65 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×#100 | C2 | semidirect |
| 3. C2×#834 | C2 | semidirect |
| 4. #4476 | C2 | semidirect |
| 5. #4475 | C2 | semidirect |
| 8. C22×#67 | C4 | semidirect |
| 12. C2×#217 | C4 | semidirect |
| 15. #937 | C4 | semidirect |
| 17. #935 | C4 | semidirect |
| 25. C2×#100 | D3 | semidirect |
| 31. C23×D3 | C2×C4 | semidirect |
| 47. C22×Dic3 | C2×C4 | semidirect |
| 56. #217 | C2×C4 | semidirect |
| 57. #217 | C2×C4 | semidirect |
| 243. C3 | #2121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5804 | 2 |
| C2×C3×#100 | 2 |
| C2×#834 | 2 |
| #4476 | 2 |
| #4475 | 2 |
| #2121 | 3 |