Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
404 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 3. C3×H(3,ℤ/4) | C2 | semidirect |
| 4. #4557 | C2 | semidirect |
| 5. #4531 | C2 | semidirect |
| 14. C2×ΓL(1,𝔽25) | C4 | semidirect |
| 15. C2×D3×C8 | C4 | semidirect |
| 20. #872 | C4 | semidirect |
| 21. C42×D3 | C4 | semidirect |
| 26. H(3,ℤ/4) | D3 | direct (N × H) |
| 40. C2×C3×C8 | C2×C4 | semidirect |
| 43. C3×C42 | C2×C4 | semidirect |
| 49. C4×Dic3 | C2×C4 | semidirect |
| 51. C2×C3⋊C8 | C2×C4 | semidirect |
| 117. C2×C8 | C4×D3 | semidirect |
| 126. C42 | C4×D3 | semidirect |
| 179. D3 | H(3,ℤ/4) | direct (N × H) |
| 198. C3 | C2×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| D3×#117 | 2 |
| C3×H(3,ℤ/4) | 2 |
| #4557 | 2 |
| #4531 | 2 |
| C2×H(3,ℤ/4) | 3 |