Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
438 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 69 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×#99 | C2 | semidirect |
| 3. C2×#833 | C2 | semidirect |
| 4. #4471 | C2 | direct (N × H) |
| 6. C24×D3 | C4 | semidirect |
| 10. C2×#217 | C4 | semidirect |
| 13. #937 | C4 | semidirect |
| 18. C3×#99 | C22 | semidirect |
| 20. #833 | C22 | semidirect |
| 23. C2×#99 | D3 | semidirect |
| 32. C23×D3 | C2×C4 | semidirect |
| 48. #217 | C2×C4 | semidirect |
| 68. #99 | C2×D3 | semidirect |
| 208. C2×C3 | AΣL(1,𝔽16) | semidirect |
| 239. C3 | C2×AΣL(1,𝔽16) | semidirect |
| 247. C2 | #4471 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#937 | 2 |
| C2×C3×#99 | 2 |
| C2×#833 | 2 |
| #4471 | 2 |
| C2×AΣL(1,𝔽16) | 3 |