Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
182 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 67 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. #4688 | C2 | semidirect |
| 3. C8×D12 | C2 | semidirect |
| 4. C3×#322 | C2 | semidirect |
| 5. #4459 | C2 | semidirect |
| 6. #4459 | C2 | semidirect |
| 7. #4458 | C2 | semidirect |
| 30. #322 | D3 | semidirect |
| 75. D12 | M16 | semidirect |
| 84. C3×C8 | D8 | semidirect |
| 141. C8 | D24 | semidirect |
| 161. C3 | #1581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D24 | 2 |
| #4688 | 2 |
| C8×D12 | 2 |
| C3×#322 | 2 |
| #4459 | 2 |
| #4458 | 2 |
| #1581 | 3 |