Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
356 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 3. #5116 | C2 | semidirect |
| 4. C2×#818 | C2 | semidirect |
| 5. #4850 | C2 | semidirect |
| 6. #4722 | C2 | semidirect |
| 7. C4×Dic12 | C2 | semidirect |
| 8. #4682 | C2 | semidirect |
| 78. C3×D4 | Q16 | semidirect |
| 132. D4 | Dic12 | semidirect |
| 162. C3 | #3338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5543 | 2 |
| C3×C8×D4 | 2 |
| #5116 | 2 |
| C2×#818 | 2 |
| #4850 | 2 |
| #4722 | 2 |
| C4×Dic12 | 2 |
| #4682 | 2 |
| #3338 | 3 |