Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4×D3×Q8 | C2 | semidirect |
| 3. C3×#460 | C2 | semidirect |
| 4. #5170 | C2 | semidirect |
| 5. #5164 | C2 | semidirect |
| 6. #5075 | C2 | semidirect |
| 7. #5021 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 10. #4774 | C2 | semidirect |
| 11. #4757 | C2 | semidirect |
| 50. #460 | D3 | semidirect |
| 129. C3×Q8 | #41 | semidirect |
| 156. Dic6 | #41 | semidirect |
| 225. Q8 | #237 | semidirect |
| 275. C3 | #3112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5716 | 2 |
| C4×D3×Q8 | 2 |
| C3×#460 | 2 |
| #5170 | 2 |
| #5164 | 2 |
| #5075 | 2 |
| #5021 | 2 |
| #4850 | 2 |
| #4835 | 2 |
| #4774 | 2 |
| #4757 | 2 |
| #3112 | 3 |