Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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×#127 | C2 | semidirect |
| 2. C2×#932 | C2 | semidirect |
| 3. C4×#235 | C2 | semidirect |
| 4. #5215 | C2 | semidirect |
| 5. #5075 | C2 | semidirect |
| 6. #5072 | C2 | semidirect |
| 7. #4924 | C2 | semidirect |
| 16. C2×#214 | C22 | semidirect |
| 18. C2×#213 | C22 | semidirect |
| 22. C4×D12 | C22 | semidirect |
| 25. C4×Dic6 | C22 | semidirect |
| 26. #832 | C22 | semidirect |
| 27. C4⋊(C3⋊C8) | C22 | semidirect |
| 29. C2×#127 | D3 | semidirect |
| 47. #235 | D4 | semidirect |
| 105. D12 | C2×D4 | semidirect |
| 109. Dic6 | C2×D4 | semidirect |
| 151. C3×C4 | AGL(1,ℤ/8) | semidirect |
| 199. C4 | #932 | semidirect |
| 203. C3 | #3038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| C2×#932 | 2 |
| C4×#235 | 2 |
| #5215 | 2 |
| #5075 | 2 |
| #5072 | 2 |
| #4924 | 2 |
| #3038 | 3 |