Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×Dic6 | C2 | semidirect |
| 4. #5166 | C2 | semidirect |
| 5. #5164 | C2 | semidirect |
| 7. C4×#216 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 10. #4765 | C2 | semidirect |
| 11. #4759 | C2 | semidirect |
| 232. C3 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5713 | 2 |
| Q8×Dic6 | 2 |
| C3×#460 | 2 |
| #5166 | 2 |
| #5164 | 2 |
| #5070 | 2 |
| C4×#216 | 2 |
| #4850 | 2 |
| #4831 | 2 |
| #4765 | 2 |
| #4759 | 2 |
| #3375 | 3 |