Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 370 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 |
|---|---|---|
| 2. #5570 | C2 | semidirect |
| 3. C3×C8×Q8 | C2 | semidirect |
| 4. #4851 | C2 | semidirect |
| 7. #4681 | C2 | semidirect |
| 30. C8×Q8 | D3 | semidirect |
| 68. C3×Q8 | SD16 | semidirect |
| 117. Q8 | #204 | semidirect |
| 144. C3 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D12 | 2 |
| #5570 | 2 |
| C3×C8×Q8 | 2 |
| #4851 | 2 |
| #4841 | 2 |
| C4×#204 | 2 |
| #4681 | 2 |
| #3359 | 3 |