Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×C3×C4×D4 | C2 | semidirect |
| 2. C22×#214 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. #5016 | C2 | direct (N × H) |
| 6. C2×#810 | C2 | semidirect |
| 7. C2×#809 | C2 | semidirect |
| 8. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 15. C3×C4×D4 | C22 | semidirect |
| 20. C2×#214 | C22 | semidirect |
| 28. #875 | C22 | semidirect |
| 29. #810 | C22 | semidirect |
| 30. #809 | C22 | semidirect |
| 31. C4⋊(C3⋊C8) | C22 | semidirect |
| 35. C2×C4×D4 | D3 | semidirect |
| 87. C4×D4 | C2×D3 | semidirect |
| 216. C2×C3 | #463 | semidirect |
| 240. C3 | C2×#463 | semidirect |
| 243. C2 | #5016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×D4 | 2 |
| C22×#214 | 2 |
| C22×#213 | 2 |
| C2×#875 | 2 |
| #5016 | 2 |
| C2×#810 | 2 |
| C2×#809 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#463 | 3 |