Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 648 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. C22×C3×D8 | C2 | semidirect |
| 2. C2×#940 | C2 | semidirect |
| 3. C2×D4×Dic3 | C2 | semidirect |
| 4. C22×#213 | C2 | semidirect |
| 5. C2×#832 | C2 | semidirect |
| 6. #5150 | C2 | direct (N × H) |
| 7. C2×#821 | C2 | semidirect |
| 8. C2×Dic3⋊C8 | C2 | semidirect |
| 17. C2×C3×D8 | C22 | semidirect |
| 21. #940 | C22 | semidirect |
| 23. D4×Dic3 | C22 | semidirect |
| 25. C2×#213 | C22 | semidirect |
| 29. #832 | C22 | semidirect |
| 30. #821 | C22 | semidirect |
| 31. Dic3⋊C8 | C22 | semidirect |
| 33. C22×D8 | D3 | semidirect |
| 48. C2×C3×D4 | D4 | semidirect |
| 85. C2×D8 | C2×D3 | semidirect |
| 116. C3×D4 | C2×D4 | semidirect |
| 127. C2×Dic3 | D8 | semidirect |
| 151. C2×D4 | #67 | semidirect |
| 192. Dic3 | C2×D8 | semidirect |
| 216. D4 | C2×#67 | semidirect |
| 232. C2×C3 | #459 | semidirect |
| 259. C3 | C2×#459 | semidirect |
| 263. C2 | #5150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| C2×#940 | 2 |
| C2×D4×Dic3 | 2 |
| C22×#213 | 2 |
| C2×#832 | 2 |
| #5150 | 2 |
| C2×#821 | 2 |
| C2×Dic3⋊C8 | 2 |
| C2×#459 | 3 |