Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
168 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 73 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. #5024 | C2 | semidirect |
| 4. #4535 | C2 | semidirect |
| 6. #4457 | C2 | semidirect |
| 7. #4454 | C2 | semidirect |
| 83. C3⋊C8 | SD16 | semidirect |
| 150. C3 | #1582 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×SD16 | 2 |
| #5024 | 2 |
| D4×C3⋊C8 | 2 |
| #4535 | 2 |
| D4⋊(C3⋊C8) | 2 |
| #4457 | 2 |
| #4454 | 2 |
| #1582 | 3 |