Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #5116 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4850 | C2 | semidirect |
| 7. #4849 | C2 | semidirect |
| 8. #4739 | C2 | semidirect |
| 9. #4722 | C2 | semidirect |
| 10. C4×Dic12 | C2 | semidirect |
| 11. #4681 | C2 | semidirect |
| 118. C3×D4 | Q16 | semidirect |
| 203. D4 | Dic12 | semidirect |
| 240. C3 | #3299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5543 | 2 |
| D4×Dic6 | 2 |
| C3×C8×D4 | 2 |
| #5116 | 2 |
| C2×#816 | 2 |
| #4850 | 2 |
| #4849 | 2 |
| #4739 | 2 |
| #4722 | 2 |
| C4×Dic12 | 2 |
| #4681 | 2 |
| #3299 | 3 |