Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. C3×#477 | C2 | semidirect |
| 4. #5091 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 7. #4873 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 11. #4790 | C2 | semidirect |
| 48. #477 | D3 | semidirect |
| 146. C4×D3 | Q16 | semidirect |
| 260. C3 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×D3×Q8 | 2 |
| C3×#477 | 2 |
| #5091 | 2 |
| #5031 | 2 |
| #4884 | 2 |
| #4873 | 2 |
| #4849 | 2 |
| #4833 | 2 |
| #4809 | 2 |
| #4790 | 2 |
| #3104 | 3 |