Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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. #5470 | C2 | semidirect |
| 3. C3×#432 | C2 | semidirect |
| 4. #4845 | C2 | semidirect |
| 5. #4739 | C2 | semidirect |
| 7. #4715 | C2 | semidirect |
| 8. #4714 | C2 | semidirect |
| 18. C2×Dic12 | C22 | semidirect |
| 25. #869 | C22 | semidirect |
| 26. #869 | C22 | semidirect |
| 28. C4×Dic6 | C22 | semidirect |
| 29. C3×C4⋊C8 | C22 | semidirect |
| 31. C3×#97 | C22 | semidirect |
| 33. #816 | C22 | semidirect |
| 41. #432 | D3 | semidirect |
| 93. C4⋊C8 | C2×D3 | semidirect |
| 97. #97 | C2×D3 | semidirect |
| 219. C3 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| #5470 | 2 |
| C3×#432 | 2 |
| #4845 | 2 |
| #4739 | 2 |
| #4731 | 2 |
| #4715 | 2 |
| #4714 | 2 |
| #3215 | 3 |