Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 3. Q8×C3⋊C8 | C2 | semidirect |
| 4. #5020 | C2 | semidirect |
| 6. #4486 | C2 | semidirect |
| 7. #4480 | C2 | semidirect |
| 67. C3×Q8 | SD16 | semidirect |
| 85. C3⋊C8 | SD16 | semidirect |
| 121. Q8 | #214 | semidirect |
| 154. C3 | #1666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#460 | 2 |
| #5076 | 2 |
| Q8×C3⋊C8 | 2 |
| #5020 | 2 |
| #4544 | 2 |
| #4486 | 2 |
| #4480 | 2 |
| #1666 | 3 |