Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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. C3×#390 | C2 | semidirect |
| 3. C2×#832 | C2 | semidirect |
| 4. C2×#809 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 6. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #4529 | C2 | semidirect |
| 31. #390 | D3 | semidirect |
| 113. C2×C3×C4 | D8 | semidirect |
| 228. C2×C4 | #213 | semidirect |
| 275. C3 | #2054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#213 | 2 |
| C3×#390 | 2 |
| C2×#832 | 2 |
| C2×#809 | 2 |
| #4939 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4529 | 2 |
| #2054 | 3 |