Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 4. #5137 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #4851 | C2 | semidirect |
| 7. #4849 | C2 | semidirect |
| 8. #4739 | C2 | semidirect |
| 9. #4723 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 238. C3 | #3328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5542 | 2 |
| D4×Dic6 | 2 |
| C3×#436 | 2 |
| #5137 | 2 |
| #5120 | 2 |
| #4851 | 2 |
| #4849 | 2 |
| #4739 | 2 |
| #4723 | 2 |
| C4×Dic12 | 2 |
| #4681 | 2 |
| #3328 | 3 |