Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 2. C22×C4⋊Dic3 | C2 | semidirect |
| 3. C3×#407 | C2 | semidirect |
| 4. #5133 | C2 | semidirect |
| 5. #5121 | C2 | semidirect |
| 6. #4736 | C2 | semidirect |
| 7. #4735 | C2 | semidirect |
| 8. #4722 | C2 | semidirect |
| 9. #4721 | C2 | semidirect |
| 32. #821 | C22 | semidirect |
| 33. #818 | C22 | semidirect |
| 34. #817 | C22 | semidirect |
| 35. #816 | C22 | semidirect |
| 44. #407 | D3 | semidirect |
| 253. C3 | #3092 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5791 | 2 |
| C22×C4⋊Dic3 | 2 |
| C3×#407 | 2 |
| #5133 | 2 |
| #5121 | 2 |
| #4736 | 2 |
| #4735 | 2 |
| #4722 | 2 |
| #4721 | 2 |
| #3092 | 3 |