Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×D3×Q16 | C2 | semidirect |
| 3. C2×C3×SD32 | C2 | semidirect |
| 4. C2×#829 | C2 | semidirect |
| 5. C2×#827 | C2 | semidirect |
| 6. #4915 | C2 | direct (N × H) |
| 7. C2×Dic24 | C2 | semidirect |
| 8. C2×#798 | C2 | semidirect |
| 17. D3×Q16 | C22 | semidirect |
| 23. C3×SD32 | C22 | semidirect |
| 25. #829 | C22 | semidirect |
| 26. #827 | C22 | semidirect |
| 28. Dic24 | C22 | semidirect |
| 29. #798 | C22 | semidirect |
| 36. C2×SD32 | D3 | semidirect |
| 83. SD32 | C2×D3 | semidirect |
| 176. C2×C3 | #510 | semidirect |
| 190. C3 | C2×#510 | semidirect |
| 193. C2 | #4915 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C2×#912 | 2 |
| C2×C3×SD32 | 2 |
| C2×#829 | 2 |
| C2×#827 | 2 |
| #4915 | 2 |
| C2×Dic24 | 2 |
| C2×#798 | 2 |
| C2×#510 | 3 |