Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C3×#460 | C2 | semidirect |
| 3. #5027 | C2 | semidirect |
| 4. Q8×C3⋊C8 | C2 | semidirect |
| 5. #4544 | C2 | semidirect |
| 6. #4485 | C2 | semidirect |
| 7. #4479 | C2 | semidirect |
| 26. #460 | D3 | semidirect |
| 69. C3×Q8 | D8 | semidirect |
| 89. C3⋊C8 | SD16 | semidirect |
| 127. Q8 | #213 | semidirect |
| 167. C3 | #1668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#460 | 2 |
| #5073 | 2 |
| #5027 | 2 |
| Q8×C3⋊C8 | 2 |
| #4544 | 2 |
| #4485 | 2 |
| #4479 | 2 |
| #1668 | 3 |