Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#568 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #5139 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 12. #947 | C4 | semidirect |
| 13. #944 | C4 | semidirect |
| 14. #940 | C4 | semidirect |
| 16. #936 | C4 | semidirect |
| 22. #568 | D3 | semidirect |
| 44. C3×M16 | D4 | semidirect |
| 113. M16 | #67 | semidirect |
| 185. C3 | #1884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#568 | 2 |
| #5832 | 2 |
| #5240 | 2 |
| #5139 | 2 |
| #4555 | 2 |
| #1884 | 3 |