Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #5518 | C2 | semidirect |
| 3. C3×#433 | C2 | semidirect |
| 4. #4847 | C2 | semidirect |
| 5. #4841 | C2 | semidirect |
| 7. #4723 | C2 | semidirect |
| 8. #4710 | C2 | semidirect |
| 9. C4×#204 | C2 | semidirect |
| 23. #870 | C22 | semidirect |
| 24. #869 | C22 | semidirect |
| 25. C4×Dic6 | C22 | semidirect |
| 26. C3×C4⋊C8 | C22 | semidirect |
| 28. C3×#97 | C22 | semidirect |
| 29. C3×C4×C8 | C22 | semidirect |
| 32. #818 | C22 | semidirect |
| 33. #817 | C22 | semidirect |
| 34. #816 | C22 | semidirect |
| 35. #816 | C22 | semidirect |
| 44. #433 | D3 | semidirect |
| 90. C4⋊C8 | C2×D3 | semidirect |
| 96. #97 | C2×D3 | semidirect |
| 97. C4×C8 | C2×D3 | semidirect |
| 200. C3 | #3123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5521 | 2 |
| #5518 | 2 |
| C3×#433 | 2 |
| #4847 | 2 |
| #4841 | 2 |
| #4731 | 2 |
| #4723 | 2 |
| #4710 | 2 |
| C4×#204 | 2 |
| #3123 | 3 |