Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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×C4×D8 | C2 | semidirect |
| 3. C4×D24 | C2 | semidirect |
| 4. #4562 | C2 | semidirect |
| 5. #4491 | C2 | semidirect |
| 6. #4490 | C2 | semidirect |
| 7. #4461 | C2 | semidirect |
| 16. #826 | C4 | semidirect |
| 23. C4×D8 | D3 | semidirect |
| 33. C3×D8 | C2×C4 | semidirect |
| 42. D24 | C2×C4 | semidirect |
| 44. C3⋊C16 | C2×C4 | semidirect |
| 80. D8 | C4×D3 | semidirect |
| 137. C3 | #2177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D8 | 2 |
| C2×#826 | 2 |
| C4×D24 | 2 |
| #4562 | 2 |
| #4491 | 2 |
| #4490 | 2 |
| #4461 | 2 |
| #2177 | 3 |