Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5477 | C2 | semidirect |
| 3. #5217 | C2 | semidirect |
| 4. #5073 | C2 | semidirect |
| 5. #5072 | C2 | semidirect |
| 6. #5070 | C2 | semidirect |
| 7. #4925 | C2 | semidirect |
| 18. C2×#213 | C22 | semidirect |
| 22. #874 | C22 | semidirect |
| 24. C4×D12 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 26. #832 | C22 | semidirect |
| 28. C4⋊(C3⋊C8) | C22 | semidirect |
| 29. C4×C3⋊C8 | C22 | semidirect |
| 31. C2×#127 | D3 | semidirect |
| 102. C2×C3×C4 | D8 | semidirect |
| 186. C2×C4 | #213 | semidirect |
| 218. C3 | #3205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#127 | 2 |
| #5477 | 2 |
| #5217 | 2 |
| #5073 | 2 |
| #5072 | 2 |
| #5070 | 2 |
| #4925 | 2 |
| #3205 | 3 |